. Five balls of different colors 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

A. 150

B. 300

C. 200

D. none of these

 

 

Best Answer

Ans: A

One possible arrangement is

WAS

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

The other possible arrangements

WAS

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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