Question

There are three passengers on an airport shuttle bus that makes stops at four different hotels, probability that all three passengers will stay at different hotels is:

• A. 1/16
• B. 1/4
• C. 3/8
• D. 3/4

Answer 1

The correct option is C 3/8

Given,

3 passengers - 4 hotels

Total :

$1\to 4$ hotels

$2\to 4$ hotels

$3\to 4$ hotels

$4^3=64$

Favourable :

$1st\to 4$ hotels

$2nd\to 3$ hotels

$3rd\to 2$ hotels

$=4\times 3\times 2=24$

Probability = Favourable / Total

$=\frac{24}{64}=\frac{3}{8}$