Ten passengers get into an elevator on the ground floor of a $20$ floor building. What is the probability that they will all get down at different floors?

\frac{20!}{10! \times 20^{10}}

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\frac{20!}{10! \times 10! \times 20^{10}}

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\frac{20! \times 10}{10! \times 20^{10}}

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Solution

The correct option is A $\frac{20!}{10! \times 20^{10}}$
Total number of ways in which the 10 passengers can get out $= 20^{10}$
Favorable number of ways $=$ number of those cases in which not more than one passenger gets out at each floor $=^{20} P_{10} = \frac{20!}{10!}$
Required probability $= \frac{20!}{10! \times 2 0^{10}}$

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Ten passengers get into an elevator on the ground floor of a 20 floor building. What is the probability that they will all get down at different floors?

The correct option is A 20!10!×2010Total number of ways in which the 10 passengers can get out =2010Favorable number of ways = number of those cases in which not more than one passenger gets out at each floor =20P10=20!10!Required probability =20!10!×2010

Ten passengers get into an elevator on the ground floor of a $20$ floor building. What is the probability that they will all get down at different floors?