Five balls are to be placed in 3boxes

Question

Five balls are to be placed in 3boxes such that balls are different but boxes are identical

Answer 1

Assuming that no box is empty. Number of ways in which I can put 5 balls in 3 identical boxes are : $$ 1 2 2 , 113$$ Number of ways to accomplish the condition is : $$^5C_1 . ^4C_2.^2C_2 \ + \ ^5C_1 . ^4C_1.^3C_3$$ There will be no rearrangement as the boxes are identical.

You final answer is : $30 + 20 = 50$

Cheers!!

Answer 2

In first box, you could put any of the five balls, there are 5 ways to put a ball in the first box. In the second box, there are 4 ways. In the third box, there are 3 ways. So, total no. of ways to put 5 different balls in 3 identical boxes are 5*4*3=60 ways