combination gre problem # 24?

Question

How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes? Can anyone explain me why this answer is wrong: 4*4*4 ?

Answer 1

If each boy is eligible for all the prizes, the 1^st prize can be given away to any one of the boys and thus it can be given away in 3 different ways.

Similarly, the 2^nd prize can be given away to any one of them in 3 different ways again and so on.

Hence, the total number of way all 4 prizes can be given away is 3*3*3*3 = 3⁴ = 81

Answer 2

It's wrong because you have 4 prizes available only for the 1st boy. Once that prize is given, only 3 prizes remain, then 2, etc.

So, the probability is: 4*3*2, since 3 prizes remain for the 2nd boy, and 2 prizes remain for the 3rd boy.