Question:
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :
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Split 5 questions among 3 sections with each at least 1: the patterns are (3,1,1) and (2,2,1).
Updated On: Nov 5, 2026
- 2250
- 2255
- 3000
- 1500
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The Correct Option is A
Solution and Explanation
Distribution (3,1,1): choose the section giving 3 questions in 3 ways: \(3\times\binom53\times\binom51\times\binom51=3\times10\times5\times5=750\).
Distribution (2,2,1): choose the section giving 1 question in 3 ways: \(3\times\binom52\times\binom52\times\binom51=3\times10\times10\times5=1500\).
Total \(=750+1500=2250\).
Answer: (1) 2250
Distribution (2,2,1): choose the section giving 1 question in 3 ways: \(3\times\binom52\times\binom52\times\binom51=3\times10\times10\times5=1500\).
Total \(=750+1500=2250\).
Answer: (1) 2250
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