Question

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. The number of ways in which we can place the balls in the boxes so that no box remains empty is $n$ then $\frac{n}{30}$ is

Answer 1

Possible arrangement are


Case I:
No of arrangements $={{}^{5}C}_2\cdot {{}^{3}C}_2\cdot {{}^{1}C}_2\cdot \frac{3!}{2!}$

Case II:
No of arrangements $={{}^{5}C}_1\cdot {{}^{4}C}_1\cdot {{}^{3}C}_3\cdot \frac{3!}{2!}$
$\therefore n=150$