EXERCISE 7.4(Permutations and Combinations)

Exercise 7.4 ncert solutions maths class 11

Question 1: If , find .

Solution: Given that

We know that if then either or

If

On rearranging we get

Now,

Question 2: Determine if

(i)

(ii)

Solution: (i) Given that:

Substituting the formula we get

On multiplying we get

(ii) Given that:

Question 3; How many chords can be drawn through 21 points on a circle?

Solution: Given 21 points on a circle and we require two points on the circle to draw a chord

Number of chords is are

Total number of chords can be drawn are 210

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

Solution: Given 5 boys and 4 girls are in total

We can select 3 boys from 5 boys in ways

Similarly, we can select 3 boys from 4 girls in ways

Number of ways a team of 3 boys and 3 girls can be selected =

Number of ways a team of 3 boys and 3 girls can be selected is ways

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: Given 6 red balls, 5 white balls and 5 blue balls

We can select 3 red balls from 6 red balls in ways

Similarly, we can select 3 white balls from 5 white balls in ways

Similarly, we can select 3 blue balls from 5 blue balls in ways

Number of ways of selecting 9 balls is

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 =

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.

Solution: Given a deck of 52 cards

There are 4 Ace cards in a deck of 52 cards. According to question, we need to select 1 Ace card out the 4 Ace cards

Number of ways to select 1 Ace from 4 Ace cards is

More 4 cards are to be selected now from 48 cards (52 cards -4 Ace cards)

Number of ways to select 4 cards from 48 cards is

Number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination = 778320.

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: Given 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers

There are 5 players who bowl, and we can require 4 bowlers in a team of 11

Number of ways in which bowlers can be selected are:

Now other players left are (bowlers)

Since we need 11 players in a team and already 4 bowlers are selected, we need to select 7 more players from 12 .

Number of ways we can select these players are:

Total number of combinations possible are:

Number of ways we can select a team of 11 players where 4 players are bowlers from 17 players = 3960

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: Given a bag contains 5 black and 6 red balls
Number of ways we can select 2 black balls from 5 black balls are

Number of ways we can select 3 red balls from 6 red balls are

Number of ways 2 black and 3 red balls can be selected =

Number of ways in which 2 black and 3 red balls can be selected from 5 black and 6 red balls are 200

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: Given 9 courses are available and 2 specific courses are compulsory for every student Here 2 courses are compulsory out of 9 courses, so a student need to select 5 – courses

Number of ways in which 3 ways can be selected from (compulsory courses) are

Number of ways a student selects 5 courses from 9 courses where 2 specific courses are compulsory = 35

Chapter 7: permutation and combination Class 11

Exercise 7.1 ncert solutions maths class-11

Exercise 7.2 ncert solutions maths class 11

Exercise 7.3 ncert solutions maths class 11

Exercise 7.4 ncert solutions maths class 11

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