NCERT Solutions for Class 11 Maths Chapter 7 – Permutations and Combinations Ex 7.4
Page No 153:
Question 1:
If
, find
.
, find.Answer:
It is known that,
Therefore,
Question 2:
Determine n if
(i) 
(ii) 
(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.
ways.
3 girls can be selected from 4 girls in 
ways.
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.
ways.
3 balls can be selected from 5 white balls in 
ways.
ways.
3 balls can be selected from 5 blue balls in ways.
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.
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 in
ways.
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.
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.
ways.
Thus, required number of ways of choosing the programme
