12 identical balls placed in 3 distinct boxes.

Question

12 identical balls placed in 3 distinct boxes. Find the probability one box has exactly 3 balls.

Accepted Answer

$$P = \frac{{}^{12}C_3\times2^9}{3^{12}} = \frac{220\times512}{3^{12}}$$

Rewriting in the given form matches option C: $55\left(\dfrac23\right)\left(\dfrac13\right)^{11}$.

Solutions · 1