Question

In how many ways can five people be distributed in three different rooms if no room must be empty?

• A. $25$
• B. $150$
• C. $720$
• D. none of these

Answer 1

The correct option is B $150$

Total number of ways $=$ (Number of ways in which groups can be formed) $\times$ (Number of ways groups can be arranged in $43$ different room).

$=[5!/3!\times 1/2!]3!+[5!/(2!{)}^2\times 1/2!]\times 3!$

$=60+90$

$=150$

Hence, the answer is $150.$