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Question

The number of ways in which n distinct objects can be put into two different boxes so that no box remains empty is

A
2n1
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B
n21
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C
2n2
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D
n22
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Solution

The correct option is C 2n2
Each object can be put either in box B1 (say) or in box B2(say). So, there are two choices for each of the n objects. Therefore the number of choices for n distinct objects is
2×2×ntimes×2=2n
One of these choices corresponds to either the first or the second box being empty.
Thus, there are 2n2 ways in which neither box is empty.

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