Seven people enter a lift. The lift stops only at three floors (which are unspecified). At each of the three floors, no one enters the lift, but at least one person leaves the lift. After the three floor stops, the lift is empty. In how many ways this can happen?

1. A1844
2. B2187
3. C1806
4. D343 x2y3z2

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Correct answer: C. 1806

Explanation

Each of the 7 people chooses one of the 3 floors, and every floor must be chosen: the number of onto functions = 3⁷ − 3·2⁷ + 3·1⁷ = 2187 − 384 + 3 = 1806.