Multiple choice

In how many ways can 'n' distinct objects be put into two different boxes such that no box remains empty?

  1. 2n – 1

  2. n2 – 1

  3. 2n – 2

  4. 2n – 3

  5. 2n
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C Correct answer
Explanation

Each of the n objects can be placed in either of the 2 boxes, giving 2^n total ways. We must exclude the 2 cases where all objects are in one box (leaving the other empty). Thus, 2^n - 2.

AI explanation

Each of the n distinct objects has 2 choices, so the total number of distributions is 2 to the power of n. This total includes 2 cases where a box is completely empty, which happens when all n objects go into a single box. Since no box can remain empty, we subtract these 2 cases from the total to get (2 to the power of n) minus 2.

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