Question

Five persons entered the lift cabin on the ground floor of $8$ floor house. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first. The probability of all five persons leaving at different floors, is

• A. $\frac{{}^8{P}_5}{7^4}$
• B. $\frac{{}^9{P}_5}{7^6}$
• C. $\frac{{}^7{P}_5}{7^5}$
• D. None of these

Answer 1

Answer: (C)

$\frac{{}^7{P}_5}{7^5}$

Beside the ground floor, there are seven floors.
The total number of ways in which each of the five persons can leave cabin at any of the $7$ floors $=7^5$.
And the favorable number of ways, that is, the number of ways, in which $5$ persons leave at different floors is ${}^7{P}_5$.
$\therefore$ The required probability $=\frac{{}^7{P}_5}{7^5}$