Quandaries
and Queries 

Question: In how many ways can 12 different fruits be distributed among 3 boys so that each receives at least 1 fruit? I solved the problem as follows The answer in my book is different.I want to know the error in my procedure. 

Hi, I bet that the answer in your book is smaller! 12 different fruits: 3 boys:  One of the 12C3 ways to pick three fruits from the 12 is to pick {A, B,  And one of the 3! ways to distribute one these among the three boys so  And one of the 3^{9} ways to distribute the remaining fruits is So the final distributlon is {A, D, E} to X, {B, F, G, H} to Y But there is at least one other way to arrive at that distribution: Therefore, your count of 12C3x3!x3^{9} counts that specific distribution Actually, the distribution {A, D, E} to X, {B, F, G, H} to Y P.S. I don't really know names of fruits starting with all Claude 

