Distribution
The number of ways to distribute 10 identical balls into 3 distinct boxes is
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- distribution
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
66
- Problem Type: Distribution of identical items into distinct groups (Balls and Boxes).
- 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.
- Identify Variables: n=10,r=3.
- Calculation:
- C(10+3−1,3−1)=C(12,2)
- =2×112×11=66.
- Logic: This accounts for boxes which might be empty.
This medium difficulty mathematics question is from the chapter permutations and combinations, covering the topic of distribution. It appeared in the 2025 exam.
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