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 floor is

• A. $\frac{{}^7{P}_5}{7^5}$
• B. $\frac{7^5}{7_5^P}$
• C. $\frac{6}{6_5^P}$
• D. $\frac{{}^5{P}_5}{5^5}$

Answer 1

The correct option is A

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

Since, if is an eight-storey building. So, there are 7 possible options for them in 7 floors in total if ground floor is not considered.

Hence, total possible outcomes

$=7\times 7\times 7\times 7\times 7=7^5$

Thus, number of ways in which 5 persons can leave from seven floors differently = ${}^7{P}_5$

$\therefore$ Required probability $=\frac{{}^7{P}_5}{7^5}$