IN HOW MANY DIFFERENT WAYS CAN 12 DIFFERENT FRUITS BE GIVEN AWAY TO 3 BOYS, SO THAT EACH BOY GETS AT LEAST ONE FRUIT?

Daer Aritra,

No. of selection of 3 fruits out of 12=¹²C₃.3 fruits can be distributed among 3 boys in 3! ways.From the remaining 9 fruits each can be distributed in 3 ways. Therefore all the 9 fruits can be distributed in 3^9 ways.
  Hence, the answer is ¹²C₃ x 3! x 3^9.

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