Question

Five of different colours are to be placed in three boxes of different sizes. Each box can hold all five . The number of ways in which we can place the in the boxes (order is not considered in the box) so that no box ** empty is

(A) 150

(B) 300

(C) 200

(D) of these

Answer 1

Correct option**(A) 150**

One possible arrangement is

| 2 | 2 | 1 |

Three such arrangements are possible.

Therefore, the number of ways is

(5C2)(3C2)(1C1)(3) = 90

The other possible arrangement,

| 1 | 1 | 3 |

Three such arrangements are possible.

In this case, the number of ways is

(5C1)(4C1)(3C3)(3) = 60

Hence, the total number of ways is

90 + 60 = 150.