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 all the balls so that no box remains empty? 

(a) 6 

(b) 36 

(c) 90 

(d) 150

Answer 1

(d) 150

As no box has to be empty, each box should have at least 1 ball. 

Let the boxes be labelled as B₁, B₂ and B₃. Then the distribution of the balls can be shown as:

∴ Number of ways of placing the balls in different boxes so that no box remains empty

= 20 + 30 + 20 + 30 + 30 + 20 = 150.