Question

Seven people are in an elevator which stops at ten floors. In how many ways can they get off the elevator?

Answer 1

The number of ways people can get off the elevator is 604800 ways.

In this question,

Number of people, n = 7

Number of floors, r = 10

The first person can leave elevator in one of 10 ways. Then second person has to choose from one of remaining 9 floors. Then third person in 8, fourth in 7 ways and so on.

Number of ways people can get off the elevator can be calculated as

⇒ $nP_r=\frac{n!}{(n-r)!}$

⇒ $10P_{7}=\frac{10!}{(10-7)!}$

⇒ $10P_{7}=\frac{10!}{(3)!}$

⇒ $10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}$

⇒ $10P_{7}=(10)(9)(8)(7)(6)(5)(4)$

⇒ 604800 ways.

Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.

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