Revision Notes for CBSE Class 11 Maths Chapter 6 (Permutations and Combinations) - Free PDF Download






FAQs on Permutations and Combinations Class 11 Notes CBSE Maths Chapter 6 [Free PDF Download]
1. Find the total number of permutations and combinations if the value of n is 12 and the value of r is 2.
We know that n = 12 and r = 2
By using the formula for permutation, we will get:
nPr = (n!) / (n - r)! = (12!) / (12 - 2)! = 12! / 10! = (12 x 11 x 10!) / 10! = 132
If we use the formula for combination, then we will get:
nCr = n1 / r! (n - 1)! . 12! / 2! (12 - 2)! = 12! / 2! (10)! = 12 x 11 x 10! / 2! (10)! = 66
2. You know that in a dictionary all permutations of the letters that are used in the word AGAIN are arranged in a particular order. Find out the 49th word by using this information.
Let’s start with the letter A. If we arrange the other four letters, then we get G, A, I, N - 4! = 24. These are the first 24 words.
Now, let’s start with the letter G. If we arrange it as A, A, I, and N in various ways, then we will get 4! / 2! = 12. These are the next 12 words.
Finally, let’s begin with the letter I. If we arrange the letters in the order of A, A, G, and N in various ways, then we will get 4! / 2! = 12. There are the next 12 words.
Hence, 24 + 12 + 12 = 48. These are the 48th word. This is why we can say that the 49th word is ‘NAAGI.’
3. There is a group of nine men and twelve women. Calculate the number of ways in which a committee of five men and three women can be chosen from the given group.
If we choose five men out of nine men = 9C5 ways = 126 ways
If we choose 3 women out of 12 women = 12C3 ways = 220 ways
Hence, the committee can be chosen in 27720 ways!
4. Define permutation and combination.
Permutation can be defined as the process of arranging numbers or objects in a particular order. Combination, on the other hand, can be defined as the method of picking items or numbers from a collection of things in a manner in which the order of the objects is not a significant consideration.
5. What are the formulas for calculating permutations and combinations?
The formula for calculation permutations is: nPr = n! / (n - r)!
The formula for calculating combinations is: nCr = n! / [r! (n - r)!]
6. In what manner are both permutations and combinations related to one another?
The formula that shows the relationship between permutations and combinations is:
nCr = nPr / r!

















