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An elevator starts with m passengers and...

An elevator starts with m passengers and stops at n floors `(m le n)` .the probability that no two passengers alight at same floor is :

A

`(.^(n)P_(m))/(m^(n))`

B

`(.^(n)P_(m))/(n^(m))`

C

`(.^(n)C_(m))/(m^(n))`

D

`(.^(n)C_(m))/(n^(m))`

Text Solution

Verified by Experts

The correct Answer is:
B
Since a person can alight at any one of n floors. Therefore, the number of ways in which m pasengers can alight at n floors is `nxxnxxn.. Xx n= n^(m)`.
The number of ways in which all passengers can alight at different floors is `.^(n)C_(m)xx m!= .^(n)P_(m)`
Hence, required probability `=(.^(n)P_(m))/(n^(m))`
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OBJECTIVE RD SHARMA ENGLISH-PROBABILITY -Chapter Test
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