Four different items have to be placed in three different boxes. In how many ways can it be done such that any box can have any number of items?

3^{4}

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4^{3}

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^{4} P_{3}

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^{4} C_{3}

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Solution

The correct option is A $3^{4}$
We have to keep $4$ different items in $3$ different boxes.
First item can be placed in any one of the $3$ boxes in $1 + 1 + 1 = 3$ ways.
Second item can be placed in any one of the $3$ boxes in $1 + 1 + 1 = 3$ ways.
Similarly, the other two items can be placed in $3$ ways each.
Number of ways to put $4$ items in $3$ boxes is $3.3.3.3 = 3^{4}$ ways.

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