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 floors is :

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

Answer 1

Answer: (A)

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

Suppose there are $5$ persons.

First person can leave the lift cabin in $7$ different ways.

Second person in $6$ ways, third person in $5$ ways.

Fourth person in $4$ different ways.

The fifth person in $3$ different ways.

$\therefore 7\times 6\times 5\times 4\times 3=2520=\frac{{}^5{P}_5}{5^5}.$