Question

The total number of ways in which $5$ balls of different colours can be distributed among $3$ persons so that each person gets at least one ball is

• A. 75
• B. 150
• C. 210
• D. 243

Answer 1

Answer: (B)

Description of Situation Here, $5$ distinct balls are distributed amongst $3$ persons so that each gets at least one ball. i.e. Distinct $\to$ Distinct
So, we should make cases

$=\left({}^5{C}_1\cdot {}^4{C}_1\cdot {}^3{C}_3\times \frac{3!}{2!}\right)+\left({}^5{C}_1\cdot {}^4{C}_2\cdot {}^2{C}_2\times \frac{3!}{2!}\right)$
$=60+90=150$