Question

An elevator contains $5$ passengers and stops at $10$ floors. The probability that no two passengers get down at the same floor is

• A. $\frac{5}{10}$
• B. $1-\frac{5}{10}$
• C. $\frac{10P_5}{{10}^5}$
• D. $1-\frac{10P_5}{{10}^5}$

Answer 1

The correct option is C $\frac{10P_5}{{10}^5}$

Total ways in which one passenger can stop $=10$
Total ways in which $5$ passengers can stop $=10\ast 10\ast 10\ast 10\ast 10$
$={10}^5$
We will select $5$ floors from $10$ floors and assign each individual to each floor to keep everyone isolated from each other
No. of ways in which no two persons stop at the same floor $=10C_5\ast 5!$
$=10P_5$
$\Rightarrow P\left(E\right)=10P_5/{10}^5$