Question

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five. In how many different ways can we place the balls so that no box remains empty?

Answer 1

Since, each box can hold five balls.
$\therefore $ Number of ways in which balls could be distributed so that none is empty, are $(2, 2, 1)$ or $(3, 1, 1)$.
i.e.,, $ ({}^5C_2 \,{}^3C_2 \,{}^1C_1 + \,{}^5C_3 \,{}^2C_1 \,{}^1C_1) \times 3!$
$= (30 + 20) \times 6 = 300$