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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 in 2 ways (Box 1 or Box 2).

The number of ways in which object can be put in=2×2×2×...2 (n times) =2n.

Two of these choices correspond to either first or the second box is empty.

(i.e., Box 1=0, Box 2=n and Box 1=n, Box 2=0)

Required number of ways 2n2.

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