Question

Five balls are to be placed in three boxes. Each box can hold all the five balls so that no box remains empty.

If balls and boxes are identical then number of ways is

Answer 1

If no box remains empty, then we can have $(1,1,3)$ or $(1,2,2)$ distribution pattern.

When balls as well as boxes are identical, we have only two ways $(1,1,3)$ and $(1,2,2)$. Hence, number of ways is $2$.