Question

$5$ balls of different colours are to be kept in $3$ boxes of different sizes. Each box can hold all five balls. Number of ways in which the balls can be kept in the boxes so that no box remain empty is

• A. $60$
• B. $90$
• C. $150$
• D. $200$

Answer 1

Answer: (C)

$150$

Arrangement of balls in three boxes:

Let boxes be $A,B,C$

Case I:

$A,B,C:1,1,3$ Total $3$ cases possible.

Total ways for this case: $3\times {}^5{C}_3{}^2{C}_1{}^1{C}_1=3\times 10\times 2=60$

Case II:

$A,B,C:1,2,2$ Total $3$ cases possible

Total ways for this case: $3\times {}^5{C}_2{}^3{C}_2{}^1{C}_1=3\times 10\times 3=90$

Total ways: $60+90=150$