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

•  \[\frac{{^7}{}{P}_5}{7^5}\]

•  \[\frac{7^5}{{^7}{}{P}_5}\]

•  \[\frac{6}{{^6}{}{P}_5}\]

• \[\frac{{^5}{}{P}_5}{5^5}\]

   

Answer 1

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