Distribution
The number of ways to distribute 10 identical balls into 3 distinct boxes is
Select the correct option:
Solution
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.
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More distribution Practice Questions
A binomial random variable representing successes in n trials has mean equal to 4 and variance equal...
A binomial random variable representing successes in n trials has mean equal to 4 and variance equal...
In a binomial setting where a marksman hits a target with probability 1/4 on each independent shot, ...
In a binomial setting where a marksman hits a target with probability 1/4 on each independent shot, ...
A biased coin showing heads with probability 1/3 is tossed five independent times in succession; wha...
A biased coin showing heads with probability 1/3 is tossed five independent times in succession; wha...
The number of ways to place 5 distinct letters into 3 distinct mailboxes, where any mailbox may rece...
The number of ways to place 5 distinct letters into 3 distinct mailboxes, where any mailbox may rece...
In a binomial distribution, the number of trials is denoted by
In a binomial distribution, the number of trials is denoted by
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.
Looking for more practice? Explore all mathematics questions or browse permutations and combinations questions on RankGuru.