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

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 11 |

Subject | Maths |

Chapter | Chapter 7 |

Exercise | Class 11 Maths Chapter 7 Permutations and Combinations Exercise 7.4 |

Number of Questions Solved | 9 |

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

**NCERT TEXTBOOK EXERCISES**

**Ex 7.4 Class 11 Maths Question 1.**

lf ^{n}C_{8} = ^{n}C_{2}, find ^{n}C_{2}.

**Solution.**

We have, ^{n}C_{8} = ^{n}C_{2}

**Ex 7.4 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 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 = ^{2n}C_{2}

$=\frac { 21! }{ 2!19! } =\frac { 21\times 20 }{ 2 } =210$

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

∴ Required number of ways of team selection = ^{5}C_{3} x ^{4}C_{3} = $\frac { 5! }{ 2!3! } \times \frac { 4! }{ 3!1! }$

=5×4/2×4=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.**

No. of ways of selecting 3 red balls =^{6}C_{3}

No. of ways of selecting 3 white balls = ^{5}C_{3}

No. of ways of selecting 3 blue balls = ^{5}C_{3}

∴ Required no. 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 no. of cards = 52

No. of ace cards = 4

No. 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 no. of ways of selecting 5 cards

**Ex 7.4 Class 11 Maths Question 7.**

In Kbw 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 players = 17, No. of bowlers = 5,

No. of non-bowlers = 12

No. of ways of selecting 4 bowlers = ^{5}C_{4}

No. of ways of selecting 7 non-bowlers = ^{12}C_{7}

∴ Required no. 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.**

No. of ways of selecting 2 black balls = ^{5}C_{2}

No. of ways of selecting 3 red balls = ^{6}C_{3}

∴ Required no. of ways of selecting 2 black & 3 red balls = ^{5}C_{2} x ^{6}C_{3}

$=\frac { 5! }{ 2!3! } \times \frac { 6! }{ 3!3! } =\frac { 5\times 4 }{ 2 } \times \frac { 6\times 5\times 4 }{ 3\times 2 } =200$

**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 no. of courses = 9

No. of compulsory courses = 2

So, the student will choose 3 courses out of 7 courses [non-compulsory courses].

∴ Required no. of ways a student can choose a programme = ^{7}C_{3} = $\frac { 7! }{ 3!4! } =\frac { 7\times 6\times 5 }{ 6 } =35$

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

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