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Question
Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is
Options
\[\frac{^{7}{}{P}_5}{7^5}\]
\[\frac{7^5}{^{7}{}{P}_5}\]
\[\frac{6}{^{6}{}{P}_5}\]
\[\frac{^{5}{}{P}_5}{5^5}\]
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Solution
\[\frac{^{7}{}{P}_5}{7^5}\]
Since, it is an eight-storey building.
So, there are 7 possible options for them in 7 floors in total if ground floor is not considered.
Hence, total possible outcomes = 7× 7× 7 × 7 × 7= 75
Thus, number of ways in which 5 persons can leave from seven floors differently = 7P5
∴ Required probability = \[\frac{^{7}{}{P}_5}{7^5}\]
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