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In how many ways can 3 prizes be distributed among 4 boys,when no boy gets all the prizes
The first prize can be given away in 4 ways as it may be given to any one of the four boys.
The second prize can also be given away in 4 ways.
Since it may be obtained by the boy who has already received a prize.
Similarly , third prize can be given away in 4 ways.
Hence the number of ways in which all the prizes can be given away = 4 x 4 x 4 = 64
Since any one of the 4 boys may get all the prizes , 
So , the number of ways in which a boy get all the three prizes = 4
So , the number of ways in which a boy does not get all the prizes = 64 - 4 = 60


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