I think I'm interpreting your problem correctly. I'm interpreting it as the simple way that 3 of the boys will get 1 prize and one of the boys will get 2 prizes. If that's the correct interpretation, then, Choose the lucky boy to get 2 prizes 4 ways. Choose the 2 prizes the lucky boy is to get 5C2 = 10 ways. Distribute the remaining 3 prizes among the other 3 boys in 3! or 6 ways. Answer 4*10*6 = 240 ways. [If that's not the correct interpretation and you are studying partitions, which are a little more advanced, and allow that the first boy can take as many prizes as he likes, and that it may even be that he takes them all and the others get none, then it's a more complicated problem. Let me know in the thank-you note form below if you meant this more complicated case. Also if this is the case, tell me whether the prizes are distinguishable or all the prizes are exactly the same.] Edwin