EXERCISE 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 in
ways.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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