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

Show whatever you have tried. – StubbornAtom Nov 13 '16 at 14:30 — StubbornAtom, Nov 13 '16 at 14:30
This is a statement, not a question. – Mårten W Nov 13 '16 at 14:51 — Mårten W, Nov 13 '16 at 14:51

score 1 · Answer 1 · answered Nov 13 '16 at 14:33

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

score 0 · Answer 2 · answered Nov 13 '16 at 14:29

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!!

Five balls are to be placed in 3boxes

2 Answers2