NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Ex 6.4 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths chapter 6 Permutations and Combinations Ex 6.4.

**NCERT Solutions for Class 11 Maths Chapter 6 ****Permutations and Combinations**** Ex 6.4**

**Ex 6.4 Class 11 Maths Question 1.**

lf ^{n}C

_{8}=

^{n}C

_{2}, find

^{n}C

_{2}.

**Solution.**

Given, ^{n}C_{8} = ^{n}C_{2}

**Ex 6.4 Class 11 Maths Question 2.**

Determine n if**(i)**

^{2n}C

_{3 }:

^{n}C

_{3}= 12 : 1

**(ii)**

^{2n}C

_{3 }:

^{n}C

_{3 }= 11 : 1

**Solution.**

**Ex 6.4 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 = ^{21}C_{2}

= 21! / 2! 19! = (21 × 20)/2 = 210

**Ex 6.4 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 ^{5}C_{3} ways and 3 girls can be selected from 4 girls in ^{4}C_{3} ways.

∴ Required number of ways of team selection = ^{5}C_{3} × ^{4}C_{3} = 5! / 2! 3! × 4! / 3! 1!

= 5 × 2 × 4 = 40

** **

**Ex 6.4 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 = ^{6}C_{3}

The number of ways of selecting 3 white balls = ^{5}C_{3}

The number of ways of selecting 3 blue balls = ^{5}C_{3}

∴ Required number of ways of selecting 9 balls

**Ex 6.4 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 ^{4}C_{1} ways.

Remaining 4 cards out of 48 cards can be selected in ^{48}C_{4 }ways.

∴ Required number of ways of selecting 5 cards

**Ex 6.4 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 = ^{5}C_{4}

Number of ways of selecting 7 non-bowlers = ^{12}C_{7}

∴ Required number of ways of selecting a cricket team

**Ex 6.4 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 = ^{5}C_{2}

Number of ways of selecting 3 red balls = ^{6}C_{3}

∴ Required number of ways of selecting 2 black and 3 red balls = ^{5}C_{2} × ^{6}C_{3}

= 5! / 2! 3! × 6! / 3! 3! = 5 × 2 × 5 × 4 = 200

** **

**Ex 6.4 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 = ^{7}C_{3} = 7! / 3! 4! = (7 × 6 × 5)/6 = 35

**Related Links:**

**NCERT Solutions for Maths Class 9**