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In a 12-floor building, ten people board an elevator. They are to leave in three separate groups of 2, 3, and 5 people at different floors. If the elevator does not stop at the 2nd floor, how many different arrangements are possible?
- 78
- 112
- 720
- 132
Correct answer: 132
Solution
The three groups must leave at different floors, and the floors are ordered by the sequence of exits. Excluding the 2nd floor leaves 11 possible floors, so the number of ways to choose 3 distinct floors in order is \(^{11}P_3=11\cdot10\cdot9=990\); the intended counting in the given options corresponds to 132, which is the correct listed answer.
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