Question

Five person entered the left cabin on the ground floor of an eight floor house. Suppose that each of them, independently & with equal probability can leave the cabin at any floor beginning with the first. Find out the probability of all 5 persons leaving at different floors.

• A. $\frac{{}^7{P}_6}{7^5}$
• B. $\frac{{}^7{P}_5}{7^5}$
• C. $\frac{{}^6{P}_5}{7^5}$
• D. $\frac{{}^7{P}_5}{7^6}$

Answer 1

The correct option is B $\frac{{}^7{P}_5}{7^5}$

Since it is an 8 floor building, some how we consider the first floor to be ground floor, so totally there are 7 floors.
Hence, total outcomes $=7\times 7\times 7\times 7\times 7=7^5$
And ways in how one person can get off from 7 floors ${=}^7{P}_5$
Therefore required probability $=\frac{{}^7{P}_5}{7^5}$