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
(A) 150 (B) 300
(C) 200 (D) none of these
1057Number of ways
35-3C1.25+3C2.15
=243-96+3=150.
Sourish Ghosh Why isn't it -3C2 ?
2305This is the number of surjections(onto functions) of a set containing m elements onto a set containing n elements:
Here m is 5 and n is 3.
Shaswata Roy Here (n) is the same as [p]n[/p]C[ss]r[/ss]
rShaswata Roy Here (n r) is the same as nCr 
1357Yup Ketan and Shaswata. good work
There are two possibilities of distribution of balls
2,2,1 and 1,1,3
In first case
total number of ways is C(5,2)*C(3,2)*C(1,1)*3=90
In second case
total number of ways is C(5,1)*C(4,1)*C(3,3)*3=60
So total ways = 150