distribution

Question

The number of ways to distribute 10 identical balls into 3 distinct boxes is

RankGuru · Accepted Answer

1. **Problem Type**: Distribution of identical items into distinct groups (Balls and Boxes).
2. **Stars and Bars Method**: The number of ways is given by $C(n + r - 1, r - 1)$, where $n$ is items and $r$ is groups.
3. **Identify Variables**: $n=10, r=3$.
4. **Calculation**:
   - $C(10 + 3 - 1, 3 - 1) = C(12, 2)$
   - $= \frac{12 	imes 11}{2 	imes 1} = 66$.
5. **Logic**: This accounts for boxes which might be empty.

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