NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.4

# NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.4

## NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.4

NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.4 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths chapter 7 Permutations and Combinations Ex 7.4.

### Ex 7.4 Class 11 Maths Question 1.

lf nC8 = nC2, find nC2.

Solution.
Given, nC8 = nC2

### Ex 7.4 Class 11 Maths Question 2.

Determine n if
(i) 2nC3 nC3 = 12 : 1
(ii) 2nC3 nC3 = 11 : 1

Solution.

### Ex 7.4 Class 11 Maths Question 3.

How many chords can be drawn through 21 points on a circle?

Solution.
A chord is formed by joining two points on a circle.
Required number of chords = 21C2
= 21! / 2! 19! = (21 × 20)/2 = 210

### Ex 7.4 Class 11 Maths Question 4.

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Solution.
3 boys can be selected from 5 boys in 5C3 ways and 3 girls can be selected from 4 girls in 4C3 ways.
Required number of ways of team selection = 5C3 × 4C3 = 5! / 2! 3! × 4! / 3! 1!
= 5 × 2 × 4 = 40

### Ex 7.4 Class 11 Maths Question 5.

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Solution.
The number of ways of selecting 3 red balls = 6C3
The number of ways of selecting 3 white balls = 5C3
The number of ways of selecting 3 blue balls = 5C3
Required number of ways of selecting 9 balls

### Ex 7.4 Class 11 Maths Question 6.

Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Solution.
Total number of cards = 52
Number of ace cards = 4
Number of non-ace cards = 48
One ace card out of 4 can be selected in 4C1 ways.
Remaining 4 cards out of 48 cards can be selected in 48C4 ways.
Required number of ways of selecting 5 cards

### Ex 7.4 Class 11 Maths Question 7.

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Solution.
Total number of players = 17

Number of bowlers = 5
Number of non-bowlers = 12
Number of ways of selecting 4 bowlers = 5C4
Number of ways of selecting 7 non-bowlers = 12C7
Required number of ways of selecting a cricket team

### Ex 7.4 Class 11 Maths Question 8.

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Solution.
Number of ways of selecting 2 black balls = 5C2
Number of ways of selecting 3 red balls = 6C3
Required number of ways of selecting 2 black and 3 red balls = 5C2 × 6C3
= 5! / 2! 3! × 6! / 3! 3! = 5 × 2 × 5 × 4 = 200

### Ex 7.4 Class 11 Maths Question 9.

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Solution.
Total number of courses = 9
Number of compulsory courses = 2
So, the student will choose 3 courses out of 7 courses [non-compulsory courses].
Required number of ways a student can choose a programme = 7C3 = 7! / 3! 4! = (7 × 6 × 5)/6 = 35

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