Are you intimidated by Permutations and Combinations questions in GRE Math?

Do you scratch your head every time you are solving a question on P&C?

Well, you aren’t the only one! Don’t worry, most students who prepare for the GRE are stumped by questions on Permutations and Combinations. However, P&C is an integral chapter of GRE Math.

Gaining your mastery in this topic is a decisive aspect if you wish to achieve that dream score of 170!

Download our eBOOK on “Quant handbook for a perfect 170 score“

Why Is Permutation and Combination Important in GRE Math?

GRE Math measures your competency in four primary areas: arithmetic, algebra, geometry, and data analysis. Permutation and Combination��is one concept falling under the data analysis section. But P&C is just a small part of data analysis – you will typically get only a few questions on it.

Now, we know what you are wondering: ‘Why must I focus on Permutation and Combination if it forms such an insignificant part of my GRE Math?’

Well, the answer is simple: It’s to differentiate the great from the good! If you are aiming for a high score in the Quantitative section, and have already mastered the rest of the topics such as algebra, arithmetic, and geometry; then a few questions can make a world of difference to your scores. And not just for your scores, the same few questions could make a difference between an admit into an elite institute as opposed to an admit into a mid-tier university.

It is therefore important that you familiarize yourself with the basics of Permutation and Combination, thereby raising your chances for a higher and a better GRE Quant score. And, we are here to help you do exactly that!

So, let’s begin with the basics. Permutations and Combinations are the bane of many students. But do you know the difference between permutation and combination? No? Don’t worry, you’re not alone.

What Are Permutations and Combinations?

As mentioned earlier, most students aren’t aware of the difference between the two concepts. While the difference is small, being aware of it will lead to accurately applying the correct formula at the correct junction.

Permutations: Let’s begin with Permutations. One way to think of this concept is as the number of arrangements or orderings within a fixed group.

For instance, if I have five students and wish to figure out in how many ways they can sit on five different chairs, I will have to use the permutations formula. This is because the number in the group is fixed. Secondly, we have to examine the number of ways in which we can “arrange” the students on the five chairs.

Combinations: On the other hand, the combination formula is useful when figuring out how many groups can be formed from a larger pool of people. For example, if a teacher wanted to know how many distinct groups she can form from all the people in the class, she would use combinations. The imperative word here is “distinct,” as one student can’t be in two groups at once.

To simplify:

Permutations & Combinations – GRE Math

Here is one worked out example of each kind to help you understand better.

1) In how many different ways can we award the 1st, 2nd, and 3rd place prizes among eight contestants? (Gold / Silver / Bronze)

In this question, we have to arrange 8 people in a sequence. We will use the permutations formula here since the order is important in solving this problem.

Here is how it would work out:

• For the first place spot, we have 8 people to choose from: A B C D E F G H
• As we go down the list, the number of people we have to choose from will decrease by one each time.
• Therefore, silver medal will have 7 choices: B C D E F G H. [B wins the silver]
• Bronze medal – 6 choices: C D E F G H. [C wins the bronze]
• Here you see that we picked specific people to win. We had 8 choices at first, then 7, then 6. The total number of options was 8 × 7 × 6 = 336
• But we don’t have to do 8, since we have to order only 3 out of 8 people.

Because 5 people were left after we picked 3 medals, the final formula is:

�� �� �� �� �� �� �� ����[which translates to]�� �� �� �� �� �� ��

Now, consider this question:

2) Steven draws 13 portraits for his art project. He wants to choose 8 of them for his studio art final. How many different groups of photos are possible?

If you observe carefully, this question asks about ‘groups’ and not the order in which the portraits will be chosen. Therefore, using the formula,

=��13!8! 13-8!

= 1287 different groups

Pro Tip: Always remember to ask yourself whether the order matters in the question. Be mindful while solving P&C questions, as the GRE may also combine one or more of these concepts into the same problem!

• Addition Rule: If an experiment can be performed in ‘n’ ways, and another experiment can be performed in ‘m’ ways, then either of the two experiments can be performed in (m + n) ways.
• Multiplication Rule: If an operation can be done in ‘m’ ways, while another operation can be done in ‘n’ ways, then both of the operations can be performed in m × n ways.

Take a GRE style practice quiz on Permutations & Combinations now!

��Tips to Master Permutation and Combination Questions in GRE Math

To be able to ace your GRE math, you have to be at the top of your game all the time! While this may seem daunting at first, with the right techniques and appropriate guidance, you will be surprised at how easily you can achieve a perfect score of 170 in Quant. But blind hard work isn’t enough; in fact, with an exam such as the GRE, working smarter rather than harder is the key!

To help you reach your dream score, we have compiled a list of some of the best tips and tricks you can use to ace your Quant section, especially when it comes to the dreaded P&C! Here they go…

1) Confirm That the Question Is Actually on P&C

First and foremost, it is imperative to understand whether the question itself requires you to use the concepts of Permutations and Combinations. In GRE Math, questions don’t come according to chapters or labels as is the case with your practice books. Rather, they are a concoction of different topics and concepts thrown together in a blender mix of a section! You can have a P&C question sandwiched between an arithmetic and geometry question. It is therefore important to determine whether the problem involves permutations and combinations or not, and not keep a one-dimensional mind.

One simple way to be alert to this is to, of course, look out for the word ‘����Dz������������ٲ�’ in the question statement. However, they usually won’t be so straightforward. Thus, if you cannot find the word ‘����Dz������������ٲ�’ embedded in the question, then keep an eye out for other important markers and related keywords. All of these imply the use of Permutations and Combinations.

Some of these could be:

• Event
• Outcome
• Random Selection
• Chance

2) Memorize the Formulas

The key to acing your Quant section – not just Permutations and Combinations – is memorizing your formulas. Not only is it a healthy habit, but also saves up on crucial time (remember, you only get 2 minutes per question – you can’t waste any precious seconds on recalling formulas!

According to our data, most of our top scorers actually spend more time learning the formulas and concepts rather than practicing the sums! We’ve listed some of the important formulas you can learn and keep in handy:

• The probability of an event = Favorable Number of Events Number of Total Outcomes
• Odds in favor of an event = Number of Favorable Outcomes Number of Total Outcomes
• Odds against an event = Number of Unfavorable outcomes Number of Total Outcomes

3) Pay Attention to the Language

GRE Math in your exam is as much a measure of your analytical abilities as it is about your cognitive prowess. To ace this exam, you have to always be on your toes. The test-makers don’t only want to see whether you can robotically apply formulas; rather they want to investigate whether you can comprehend what is asked of you and suitably apply your brains.

Thus, they create challenging problems by using subtle language to indicate whether you should use a combination formula, a permutation formula, or perhaps both sometimes, to answer the question on hand.

Keep in mind, combination-based questions will indicate that you need to form groups or sets, whereas permutation questions will hint towards finding an order. Words and phrases such as ‘first’, ‘second’, or ‘third’; or ‘how many different ways’ are usually indicators of permutations.

4) Practice, Practice, and more Practice!

One should always pay heed to old adages, for they hold the most wisdom. And it doesn’t get much better that, “practice makes perfect”. There is a reason this has reverberated through history; it’s because it’s true. There is no shortcut to success. The more of these problems you solve, the more you will familiarize yourself with them. By practicing more, even if you get them wrong, you will be acquainting yourself with the style of words, the diction, the way the questions are posed, and the format in which they will be presented to you.

Our data reveals that more often than not, the difficulty bar of questions on P&C is usually set at medium to high. So, make sure that you practice GRE questions which are a little tough. You must practice advanced GRE questions of level 4 and level 5 to be able to tackle the question on your D-Day head on!

Moreover, you will also be reading the corresponding explanations along with the answers, which will further help you understand the concepts of P&C better. The better prepared you are to ace Permutation and Combination questions, the higher your chances of acing your GRE Math!

Special Pointers to Follow On the D-Day

We have also put together a list of some special pointers for you to follow right before you Big Day! Consider this as a practical ‘last minute’ tips list. Read it right before you walk into your exam – and walk out with flying colors!

• Firstly, and most importantly, sleep. And sleep well. Nothing ruins your chances of getting a good score as much as a tired mind. Research has repeatedly shown the importance of a good night’s sleep before and exam. Not only does it refresh you and recharge your batteries, psychologists also say that it helps consolidate and retain memorized information better.��
• Stay calm, composed and as the famous book Hitchhiker’s Guide to the Galaxy states: Don’t Panic! Nothing shuts down your neuro-receptors faster than anxiety. If you feel stuck or are unable to solve a question, move on. Circle back to it later.
• In relation to the above point, if you still feel like you don’t know the answer to the question; then as a last resort make an educated guess (And hope Lady Luck smiles on you). After all, you miss 100% of the chances you don’t take. ����
• Go fully prepared with your stationary in place. Dress well, and eat something filling. Feeling prepared and ready is crucial! Researchers have regularly found correlations between mentally ‘feeling ready’ and associated better performance on cognitive tasks.
• Punctuality is key! The GRE is stressful as it is, so do yourself a favor and reach your test center on time. Worrying about being tardy will only disrupt your mental peace.
• When it comes to P&C, remember:

a) Re-ordering letters of a word, tossing of coins, rolling dice, and pack of cards all come under permutations.

b) Combinations are when you are asked to compute probabilities for independent events that occur together, and mutually-exclusive events.

We hope this article provided you with smart ways to crack Permutation and Combination questions in GRE Math. If you wish to take a GRE style practice quiz on this topic, you can do so here.

All the best!

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Introduction to GRE Probability

The Quants section of GRE assesses you across four broad areas- arithmetic, algebra, geometry, and data analysis. Probability is one of the concepts tested in the data analysis section. However, Probability is just a small part of data analysis and you may expect hardly two to three questions on probability.

Now, you might be asking why to study probability if it forms such an insignificant part of GRE Quants? Well, if you are aiming for a high score in the quantitative section and have already mastered the algebra, arithmetic, and geometry; then two or three questions can make a world of difference in your scores. It is therefore important that you familiarize yourself with the basics of probability thereby raising your chances for a higher and a better GRE Quants score.

Download our eBOOK on “5 Techniques to score a perfect 170 in GRE Quant“

Probability questions can take on many different forms such as multiple choice questions, quantitative comparison, and numeric entry. In case of multiple choice questions, you will be asked to select only one answer from a list of five choices. Quantitative comparison questions consist of two quantities, let’s say A and B, which are accompanied by a description. Your task is to compare the quantities and select one of the four possible choices. Numeric entry questions, as the name suggests, ask you to enter your answer either as an integer or as a decimal in an answer box or enter a fraction in two separate boxes.

Concepts tested in GRE Probability

Now that you have a fair idea about the number and kind of questions to expect, let us have a look at the concepts tested by these probability questions. All GRE probability questions will test your knowledge of two basic concepts- simple probability and permutation and combination.

Simple probability:

Probability is a way to describe uncertainty and the possible outcomes of an experiment using numbers. Simple probability determines the likelihood that an event will happen. Let us look at an example to understand simple probability better.

When we perform an experiment, then the set of all the possible outcomes is called the sample space (S). When we roll a die, the possible outcomes are 1, 2, 3, 4, 5, and 6. Here, in our example of rolling a die the sample space is-

S = {1, 2, 3, 4, 5, 6}

Any subset of the sample space is called an event. So, let’s say “rolling an even number” is an event which corresponds to the outcome of {2, 4, 6}. Now, the probability of rolling an even number is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event its ‘favourable outcomes’. So, the probability of an event is determined using the following formula-

Probability = Favourable number of events / total number of events

or, ����������P(E) =n(E) /��n(S)

Therefore, the probability of getting an even number when we roll a die is-

Probability of getting an even number = {2,4,6} /��{1,2,3,4,5,6}

= 3/6 ����

= 1/2 ����

Thus, the probability of getting an even number while rolling a die is half. Or in other words, the probability of getting an even number when we roll a die is fifty percent.

Permutation and combination:

Apart from simple probability, the GRE probability section also tests your knowledge of permutation and combinations. In very simple words, permutation refers to sequences and combination refers to groups. In a sequence order is important. Therefore, permutations are sequences where order is important, whereas in case of combinations, the order is not important. Let us understand both these concepts with the help of an example.

Consider the following question:-

In how many different ways can five people sit in a row?

In this question, we have to arrange five people in a sequence. However, the order is important in solving this problem. Now, for the first spot in the row, we have five people to choose from. As we go down the line, the number of people we have to choose from will decrease by one. Therefore, we have 5 x 4 x 3 x 2 x 1 = 120 ways in which five people can sit in a row.

Now, consider this question:-

Steven drew 13 portraits for his art project. He wants to choose 8 of them for his studio art final. How many different groups of photos are possible?

If you observe carefully, this question asks about groups and not the order in which the portraits will be chosen. Therefore, this is a combination problem. Therefore, using the formula-

nCk = n! /��k! * (n–k)!

= 13! /��8! * (13–8)!

= 1287 different groups

Download our eBOOK on “How to Master GRE Probability“

Tips to master GRE Probability questions

Tip 1- Confirm that the question is on probability:

In GRE questions don’t come labeled or tagged as arithmetic or probability. It is therefore important to determine whether the problem involves probability or not. So, look for the word ‘����Dz������������ٲ�’ in the questions. If you cannot find the word ‘����Dz������������ٲ�’ embedded in the question description then look for other important and related key terms such as- event, outcome, random selection.

Consider the following example-

1) A fair dice is tossed. Event A is defined as getting a prime number and event B is defined as getting an even number. Which one of the following is/ are true?

(i) P(B)= 1/2

(ii) P(A n B)= 0

(iii) P(A) + P(B)= 1

(iv) P(A n B)= 1/6

(v) P(A)= 4/6

Notice in this example question that the word probability has not been used. But as you can observe the word event appears in the question. This means that the question involves probability.

Tip 2- Memorize the formulas:

If you want to have a good Quants score then memorizing the key formulas in probability is important. You should not be wasting time trying to figure out what the formula was as you don’t get a lot of time to solve the questions. Our experience with GRE aspirants shows that top scorers actually spend more time learning formulas and concepts rather than practicing sums.

These are some of the important probability formulas you can memorize and keep in handy-

The probability of an event = Favourable number of event number of total outcomes

Odds in favor of an event = Number of favorable outcomesNumber of total outcomes

Odds against an event = Number of unfavorable outcomesNumber of total outcomes

Download our eBOOK on “GRE Math Formula Book for a Perfect 170“

Tip 3- Practice a lot:

There is no shortcut to success. And that is true even for GRE Quants. If you are dreaming of higher Quants score, your dream will come true with thorough practice. Data shows that difficulty level of questions on probability is usually medium to high. So, make sure that you practice GRE questions which are a little tough. You must practice advanced GRE questions of level 4 and level 5.

In order to secure a higher percentile in GRE Quants, it is important that you gain enough understanding of probability concepts. In fact, achieving a perfect 170 in Quants is not a very difficult task. What you need is some advice and guidance regarding how to prepare and avoid some common mistakes that GRE test takers often make. You can check out our video on Quant Shortcuts! (Probability)

We hope this article provided you with smart ways to crack GRE Probability questions. All the best!

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��ɫ����Ƶ alumnus, Shivang an electrical engineer from IIT Kharagpur achieved this feat with an impressive score of 324 thus comfortably cruising past the much coveted 320 mark. We at ��ɫ����Ƶ were sure Shivang’s success story could definitely inspire many students. So, we requested him to speak with us and share his experiences, tips and tricks employed during his GRE online preparation. Shivang happily accepted our request.��In a candid session with our senior GRE expert, Shivang opened up and discussed about his future plans, his preparation style, exam day experience and his success mantra.��This is how Shivang’s discussion went with senior GRE expert.

So, this is what happened during the course of discussion in words.

Introduction

GRE expert: Shivang, before we begin with the discussion why don’t you tell us something about yourself.
Shivang: Sure. I’m an Electrical Engineering student from IIT Kharagpur. I hail from a small district in North Western UP. I am an avid cricket follower and a huge fan of Dhoni and Chennai Super Kings.

GRE Score

GRE expert: Alright Shivang. Could you tell us about your GRE score?
Shivang: I achieved a GRE score of 324, with a Quant score of 170 and a Verbal score of 154. Out of 6 points in AWA I scored 3.5.

Why Ms in US

GRE expert: Why MS in US?
Shivang: I actually wanted to go for Civil Services in my pursuit for a career. But it’s not until I went to Germany for a summer internship that i changed my mind. I got really interested in the field of renewable energy. I gave a thought about the pros and cons and finally decided to pick up MS over Civil services for a career option.
Coming to why US. It has some of the finest universities in the world. Great job opportunities and highly experienced faculty are some of the other reasons for preferring US. I will also apply for European countries but my first priority is US.

Motivation behind MS

Shivang, electrical engineer, IIT Kharagpur

GRE expert: What was your motivation behind pursuing MS?
Shivang: As I have already mentioned while completing my research/project in Germany in the field of wind energy, did I realize it was my chance to pursue my masters in that field. I want to contribute something to that field, invent something, try to build something. This is what encouraged to me to go for Master’s.

Specialization

GRE expert: What field are you going to specialize in?
Shivang: I will be pursuing my MS in Electrical in the field of Power and Energy Engineering.

Plans after Master’s

GRE expert: What are your plans after Master’s?
Shivang: As of now, after my Master’s I am planning to get into a job. But I am not sure, if I like the field I’m doing my Master’s in I will probably go for a Ph.D.

Planning for GRE

GRE expert: Shivang, can you tell us how you went about planning for your GRE?
Shivang: My friends had been preparing for GRE for quite some time. One of my friend who was preparing with ��ɫ����Ƶ at that time recommended about it. So, I registered and started my preparation from the first week of September. I had booked my GRE date on 12th October. So, I had 1-1.5 months to prepare.

GRE expert: A score of 324 with 1-1.5 months of preparation, that’s brilliant Shivang!
Shivang: Thank you.

GRE Preparation

Quant��Preparation

GRE expert: Shivang can you tell us the secret behind getting a perfect 170 in GRE Quant.
Shivang: As soon as I joined ��ɫ����Ƶ, I gave my diagnostic test that helped me gauge my level and how much preparation is required to achieve my target score. I spoke to my SFAs (Personal Trainers or Student Facilitators and Analysts as we call them) and they provided a schedule which I tried to stick to. I tried to go through each and every module offered, took exams for each module, went through all of the questions even though I was pretty sure I could solve them.
I also attempted 10 GRE Quant style tests where the pattern is quite similar to the one in the actual GRE. The difficulty level of some of the questions in the ��ɫ����Ƶ module are a little bit higher than actual test, which I think is necessary so that you feel quite comfortable with all types of questions.

Verbal Preparation

“Don’t follow the crowd and work hard in what you believe”

GRE expert: Can you tell us about your Verbal preparation?
Shivang: My verbal preparation was similar to the GRE Quant preparation. I got a 149 in diagnostic test. I knew I had to pull up my socks. It’s different from Quant section. The difference is that in Quant with regular practice you’re assured to get good marks. Not so in Verbal.
I went through all the modules from text completion to reading comprehension to sentence equivalence. You have to learn a lot of words. WordBot and Wordlist helped me a lot. WordBot provides sentence usage and figures with words that makes it easier to remember the words. I learnt 500-600 words but remembering 1000 words should be fine.
Later on I went through the ETS book, you can go through that too.

AWA Preparation

GRE expert: How about your AWA preparation?
Shivang: There are two��sections when it comes to AWA. Analyzing an issue and analyzing an argument. I started with my AWA preparation 1 week before. I went through ETS and the list of topics and wrote down essays on as many topics as possible. Taking timed tests help will help manage time in the actual test. Going through samples on ETS website and focusing on your weaker section will help.

Exam Day Experience

GRE expert: How was your exam day experience?
Shivang: I live in Kharagpur and my exam center was in Kolkata, so I had left a day early and stayed in a hotel. My exam started at 8:00 AM. It was a four hour test with 10 minute break in between 2 sections. But I felt it went by really fast.

Success Mantra

Shivang: Like many others I too believe in hard-work and dedication. I don’t follow the crowd and I believe no one should. Work hard in whatever you believe. Stay motivated and work hard. You will get to success ultimately.

For any queries – Please comment below and our experts will get back to as early as possible. You can also call us on+919884453276 and speak to our GRE expert.
We hope Shivang’s story has been able to provide you the much needed push, confidence and encouragement. Happy learning with ��ɫ����Ƶ.

The post Whizzing Past 320 With 170 in GRE Quant: Shivang’s Story So Far appeared first on ��ɫ����Ƶ Blog.