Question

The number of ways in which $9$ identical balls can be placed in three identical boxes is

• A. $55$
• B. $\frac{9!}{{\left(3!\right)}^4}$
• C. $\frac{9!}{{\left(3!\right)}^3}$
• D. $12$

Answer 1

Answer: (D)

$12$

We have to average 9 identical marbles in 3 identical boxes.

Only combinations of 3 numbers whose total is 9 are to be counted.

$(9,0,0),(8,1,0),(7,2,0),(7,1,1),(6,3,0),(6,2,1),(5,4,0),(5,3,1),(5,2,2),(4,4,1),(4,3,2),(3,3,3)$

There are 12 such combinations.