In how many ways can 3 prizes be distributed among 4 girls, when
(i) no girl gets more than one prize?
(ii) a girl may get any number of prizes? and
(iii) no girl gets all the prizes?

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24, 64 and 60

22, 62 and 58

20, 60 and 56

18, 58 and 54

answer is A.

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Detailed Solution

1st case,
First prize given to any = 4 girls
Second prize given to any = 3 girls
Third prize given to = remaining 2 girls
Therefore, the number of ways to distribute the prize

= (4 \times 3 \times 2) = 24

2nd case,
Each prize given to = 4 girls
Way of prize distribution = 4 ways
Girls can receive any number of prizes then,
Number of ways to distribute the prize

= (4 \times 4 \times 4) = 64

3rd case,
Number of ways in which a girl gets all the prize = 64
Number of ways in which girls get all the prize = 4
We remove the ways
Therefore, the number of ways to distribute the prize