Question

Five balls are to be placed in three boxes. Each box can hold all the five balls. In how many different ways can we place the balls so that no box remains empty, if balls are identical and boxes are different is

Answer 1

Balls can be filled in either $\{1,1,3\}$ ways or $\{1,2,2\}$
Now for both the cases the balls can be arranged in $=\frac{3!}{2!}$
Total ways $=2\times \frac{3!}{2!}=6$

Alternate :
Balls can be filled in ${}^{n-1}{C}_{r-1}={}^4{C}_2=6$ ways.