Question

Five persons entered the lift cabin on the ground floor of an eight 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

• A. $\frac{^{7}{{P}_{5}}}{{{7}^{5}}}$
• B. $\frac{{{7}^{5}}}{^{7}{{P}_{5}}}$
• C. $\frac{6}{^{6}{{P}_{5}}}$
• D. $\frac{^{5}{{P}_{5}}}{{{5}^{5}}}$

Answer 1

Answer: (A)

$\frac{^{7}{{P}_{5}}}{{{7}^{5}}}$

Answer 2

Since, each person can leave the cabin at any floor. Total number of ways, ${{7}^{5}}$
$\therefore$ Required probability $=\frac{^{7}{{P}_{5}}}{{{7}^{5}}}$