In how many ways can 5 different fruits be distributed among four children?

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In how many ways can 5 different fruits be distributed among four children? (Some children may get more than one fruit and some may get no fruits.)

(A) 4^5
(B) 5^4
(C) 5!
(D) 4!
(E) 4!*5!


OA A

Source: Veritas Prep

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This is a 700-Level question.

There are 5 different fruits to be distributed among 4 children.
First person does not choose fruit in 5 ways. That would have been true if each child were to pick exactly 1 fruit. But here a child may not get any fruit and another may get 2 or more.

The number of ways to distribute 5 different fruits among 4 children = 4^5
Since each fruit has 4 choices for distribution.

Answer: A