# NCERT Class 11-Math՚S: Chapter – 7 Permutations and Combinations Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 23**:

In how many ways can a football team of 11 players be selected from 16 players?

How many of them will

(i) Include 2 particular players?

(ii) Exclude 2 particular players?

**Answer**:

(i) (ii)

**Question 24**:

A sports team of 11 students is to be constituted, choosing at least 5 from Class XI and atleast 5 from Class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted?

**Answer**:

**Question 25**:

A group consists of girls and boys. In how many ways can a team of 5 members be selected if the team has

(i) No girls

(ii) At least one boy and one girl

(iii) At least three girls.

**Answer**

(i)

(ii)

(iii)

## Objective Type Questions

Choose the correct answer out of the given four options against each of the Exercises from 26 to 40 (M. C. Q.) .

**Question 26**:

If then n is equal to

(A) 20

(B) 12

(C) 6

(D) 30

**Answer: (A)**

**Question 27**:

The number of possible outcomes when a coin is tossed 6 times is

(A) 36

(B) 64

(C) 12

(D) 32

**Answer: (B)**

**Question 28**:

The number of different four digit numbers that can be formed with the digits and using each digit only once is

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 29**:

The sum of the digits in unit place of all the numbers formed with the help of 3,4, 5 and 6 taken all at a time is

(A)

(B)

(C)

(D)

**Answer: (B)**

**Question 30**:

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 31**:

A five digit number divisible by 3 is to be formed using the numbers 0, 1,2, 3,4 and 5 without repetitions. The total number of ways this can be done is

(A)

(B)

(C)

(D)

[**Hint**: 5 digit numbers can be formed using digits or by using digits since sum of digits in these cases is divisible by 3.]

**Answer: (A)**