Question

In how many ways 3 prizes can be distributed among 4 boys so that no boy gets all prizes?

Answer 1

First prize can be given to any one of the 4 boys, so it can be given in 4 ways. Second prize can also be given in 4 ways, as the boy getting first prize can also get the second. Similarly, third prize can be given in 4 ways.

Hence, the total number of ways in which a boy can get any number of prizes = 4× 4 × 4 = 64

Number of ways in which a boy gets all the 3 prizes is 4, as any one of the 4 boys may get all the prizes.

Hence, the total number of ways in which a boy does not get all the prizes = 64 – 4 = 60