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. Find out the probability of all five persons leaving at different floors.

• A. $=\frac{{}^8{P}_5}{7^5}$
• B. $=\frac{{}^7{P}_5}{8^5}$
• C. $=\frac{{}^8{P}_5}{8^5}$
• D. $=\frac{{}^7{P}_5}{7^5}$

Answer 1

The correct option is D

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

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