What are CAT Permutation and Combination Questions?
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 the rearrangement of the members is called a permutation. The permutation process is the arrangement of 'r' things from one set without 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!
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Factorial in Permutation and Combination CAT Questions
Before knowing the formulas for Permutation and Combination Questions for CAT, the aspirants must know the concept of Factorial. It is important to note the concepts of Permutation and Combination CAT Questions. The 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
- 1! = 1
- 2! = 1x2 = 2
- 3! = 1x2x3 = 6
- 4! = 1x2x3x4 = 24
- 5! = 1x2x3x4x5 = 120
So the main thing to be remembered related to Permutation and Combination CAT Questions is that:
Note: 0! is always equal to 1 (The 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 CAT Questions.
Suppose there are 6 people, and we have to arrange them in 6 vacant places. So, we will start from first place, which means we will choose 1 person out of 6 for 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 the “n” number of places. Then the total number of arrangements that are done will be equal to “n”.
Permutation and Combination CAT Questions 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 exam easily.
Sample CAT Permutation and Combination Questions
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 even places. How many such arrangements are possible?
Answer: Total number of such arrangements = 2880
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
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 can you do this?
Answer: 110 ways
How to Solve Permutation and Combination CAT Questions?
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!
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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 CAT Questions
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.