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

The correct option is B

$150$

Explanation for correct option:

$5$ balls can be distributed to $3$ persons in $3^5$ ways

Number of possibilities when one person does not get any ball $={{}^{3}C}_1(2^5–2)=90$

Number of possibilities when one get all ball $={}^{3}C_1=3$

Therefore, total number of possibilities, when each person gets at least one ball $=3^5-90-3$

$$\begin{gathered} =243–93 \\ =150 \end{gathered}$$

Hence, the correct option is option(B)