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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 floors is
Options
\[\frac{{^7}{}{P}_5}{7^5}\]
\[\frac{7^5}{{^7}{}{P}_5}\]
\[\frac{6}{{^6}{}{P}_5}\]
\[\frac{{^5}{}{P}_5}{5^5}\]
Solution
\[ \frac{{^7}{}{P}_5}{\left( 7 \right)^5}\]
\[\text{ Total possible ways of leaving the lift }= 7 \times 7 \times 7 \times 7 \times 7 = \left( 7 \right)^5 \]
\[5 \text{ people can leave different floors in} {^7}{}{P}_5 \text{ ways } . \]
\[P\left( 5 \text{ people leaving the lift at different floors} \right) = \frac{{^7}{}{P}_5}{\left( 7 \right)^5}\]
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