CAT Permutation and Combination Questions with Solutions: CAT Questions

By Aditi Joshi|Updated : March 31st, 2022

Permutation and Combination CAT Questions are very interesting as the aspirants can relate these with real-life situations. Basically, Permutation and Combination are the methods to depict a group or a group of objects in a set. It defines the ways of selection & arrangements in a certain group. So, the main thing is that when we select the data from the group,  it is known as combination; while the order in which they are represented is known as permutation.

Permutation and Combination have a direct application in probability. The aspirants can expect 2-3 Permutation and Combination Questions for CAT. These questions are easier if you are well-versed with the basics, formulas, and concepts. In this article, BYJU’S Exam Prep Experts have given a detailed explanation of Permutation and Combination, including the concepts, formulas, and tips to attempt the questions.

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Understanding Permutation and Combination Questions for CAT 

As per the mathematical concept, permutation is related to the process of arranging the members of one group into a specific order or sequence. In other words, if the set is already arranged, then rearrangement of the members is called a permutation. The process of permutation is the arrangement of 'r' things from one set of things without any replacement. So, the thing is order matters a lot in the permutation process.

  •  nPr= n!/(n-r)!

On the contrary, the combination is the process of selecting the items from a collection of members. In smaller cases, you can count the combination number. It can be said that combination is the selection from 'n' objects taken 'r' at a time without any repetition. So, the combination is the choice of 'r' thing from a set of 'n' things without any type of replacement. Thereby, the order is not important in combination.

  • nCr = n!/(n-r)!r! = nPr /r!

 Check CAT Syllabus for better preparation

Factorial in Permutation and Combination Questions for CAT

Before knowing the formulas for Permutation and Combination CAT Questions, the aspirants must know the concept of Factorial. It is important to note the permutation and combination concepts. Factorial of a number 'n!' is defined as the product of first 'n' natural numbers. 

It means n! = 1x2x3x4x5x6x……………….x(n-2)x(n-1)xn

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So the main thing to be remembered is that:

Note: 0! is always equal to 1 (Factorial of a number can never be negative and Factorial is defined only for whole numbers)

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Application of Factorial in Permutation and Combination Questions for CAT 

The main use of factorial is in the arrangement. Now note the below section to know how factorial helps in the arrangement of Permutation and Combination Questions for CAT.

Suppose, there are 6 people, and we have to arrange them in 6 vacant places. So, we will start from the first place, which means we will choose 1 person out of 6 for the first place. It can be done in 6 ways.

Now only 5 places are vacant and 5 people are left. So, we will again choose 1 person out of 5 for the second place. In the same way, other persons will be arranged and placed in the left vacant places.

As, you know we have to do all these activities, so we will multiply all these ways to get the final answer.

So, the total number of ways = 6x5x4x3x2x1 = 720

Therefore, we can say that we have to arrange “n” things in “n” number of places. Then the total number of arrangements that are done will be equal to “n”.

Permutation and Combination Questions for CAT PDF 

The candidates preparing for the upcoming exam solve CAT Permutation and Combination Questions to grasp accuracy on this. Click on the link below and download Permutation and Combinations Questions to ace the CAT Exam easily.

☛ Download Permutation and Combination Questions for CAT PDF

Sample Permutation and Combination Questions for CAT

Note the below questions to get an idea of the type of questions asked from permutation and combination in the CAT Exam

Question 1: It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

Answer: Total number of such arrangements = 2880

Permutation and Combination Questions for CAT

Question 2: There are 5 girls and 4 boys in a class. In how many ways the monitor for that class can be chosen?

Answer: Number of Ways = 9

Permutation and Combination Questions for CAT

Question 3: There are 11 players in a team, from which you have to choose 1 wicketkeeper and 1 bowler. In how many different ways you can do this?

Answer: 110 ways

Permutation and Combination Questions for CAT

How to Solve Permutation and Combination Questions for CAT

The aspirants must keep in mind the below points to solve CAT Permutation and Combination Questions.

  • As per the mathematical concept, Permutation is the arrangement of the object in a definite way. So note the below formula to solve Permutation Questions:
    • nPr = n!/(n-r)!
  • The combination is the object selection without ant definite format. So, while solving Combination Questions must keep in mind the below formula:
    • nCr = n!/(n-r)!r!

Best Books for Permutation and Combination Questions for CAT

It is very important to have a good list of books to prepare Permutation and Combination Concepts. The candidates can follow the below books to prepare CAT Permutation and Combination Questions quickly. 

  • Permutation and Combinations by Ramesh Chandra
  • How to Prepare for Quantitative Aptitude for the CAT by Arun Sharma
  • Mathematics Books (Class 6 to 12) by NCERT
  • Quantitative Aptitude by R.S. Aggarwal

Key Points for Permutation and Combination Questions for CAT

Note the below points, which are necessary to solve CAT Permutation and Combination Questions smoothly.

  • Whenever it is required to arrange “n” number of things in the “n” number of places, then there are total n! number of ways of arrangement.
  • Whenever it is required to select “r” number of things out of “n”, then there is a total nCr number of ways for selection.
  • When it is required to select “r” things from “n” then we can arrange those “r” things at “n” place in total nPr ways.

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FAQs

  • As per Exam Analysis, Permutation and Combination Question For CAT is an important topic in the exam. These are completely based on the logic of combination and cases that can be formed for a certain thing to happen. Additionally, these questions are also very helpful to solve probability questions.



  • The number of questions may vary from year to year. However, the aspirants can expect 2-3 CAT Permutation and Combination Questions. This is an important topic for the upcoming exam. Solve CAT Online Test series to clear CAT Cutoff.



  • As per experts, conceptual clarity is very important for Permutation and Combination Questions for CAT. You can attend BYJU’S Exam Prep Online Classes to clear your doubts directly from the experts.



  • As per expert analysis, these questions are a little tricker rather than difficult. The aspirants need to understand the meaning of the questions to solve CAT Permutation and Combination Questions. Remember the below two formulas always to solve these questions without any stress.

    • Permutation: nPr = n!/(n-r)! 
    • Combination: nCr = n!/(n-r)!r! = nPr /r!

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