Respuesta :
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
⇒ [tex]nP_r=\frac{n!}{(n-r)!}[/tex]
⇒ [tex]10P_{7}=\frac{10!}{(10-7)!}[/tex]
⇒ [tex]10P_{7}=\frac{10!}{(3)!}[/tex]
⇒ [tex]10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}[/tex]
⇒ [tex]10P_{7}=(10)(9)(8)(7)(6)(5)(4)[/tex]
⇒ 604800 ways.
Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.
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