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

#### Page No 153:

#### Question 1:

If, find.

#### Answer:

It is known that,

Therefore,

#### Question 2:

Determine

*n*if
(i) (ii)

#### Answer:

(i)

(ii)

#### Question 3:

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

#### Answer:

For drawing one chord on a circle, only 2 points are required.

To know the number of chords that can be drawn through the given 21 points on a circle, the number of combinations have to be counted.

Therefore, there will be as many chords as there are combinations of 21 points taken 2 at a time.

Thus, required number of chords =

#### Question 4:

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

#### Answer:

A team of 3 boys and 3 girls is to be selected from 5 boys and 4 girls.

3 boys can be selected from 5 boys in ways.

3 girls can be selected from 4 girls in ways.

Therefore, by multiplication principle, number of ways in which a team of 3 boys and 3 girls can be selected

#### 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.

#### Answer:

There are a total of 6 red balls, 5 white balls, and 5 blue balls.

9 balls have to be selected in such a way that each selection consists of 3 balls of each colour.

Here,

3 balls can be selected from 6 red balls in ways.

3 balls can be selected from 5 white balls in ways.

3 balls can be selected from 5 blue balls in ways.

Thus, by multiplication principle, required number of ways of selecting 9 balls

#### Question 6:

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

#### Answer:

In a deck of 52 cards, there are 4 aces. A combination of 5 cards have to be made in which there is exactly one ace.

Then, one ace can be selected in ways and the remaining 4 cards can be selected out of the 48 cards in ways.

Thus, by multiplication principle, required number of 5 card combinations

#### 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?

#### Answer:

Out of 17 players, 5 players are bowlers.

A cricket team of 11 players is to be selected in such a way that there are exactly 4 bowlers.

4 bowlers can be selected in ways and the remaining 7 players can be selected out of the 12 players inways.

Thus, by multiplication principle, required number of ways of selecting cricket team

#### 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.

#### Answer:

There are 5 black and 6 red balls in the bag.

2 black balls can be selected out of 5 black balls in ways and 3 red balls can be selected out of 6 red balls in ways.

Thus, by multiplication principle, required number of ways of selecting 2 black and 3 red balls

#### 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?

#### Answer:

There are 9 courses available out of which, 2 specific courses are compulsory for every student.

Therefore, every student has to choose 3 courses out of the remaining 7 courses. This can be chosen in ways.

Thus, required number of ways of choosing the programme

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