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Maths-

General

Easy

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 ( order is not considered in the box) so that no box remains empty is

150
300
200
none of these

The correct answer is: 150

One possible arrangement is

Three such arrangements are possible. Therefore, the number of ways is ( ⁵C₂) ( ³C₂) ( ¹C₁) (3) = 90
The other possible arrangements

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.
Hence (a) is the correct answer.

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