Question

There are three sections in a question paper, each containing 5 questions. A candidate has to solve any 5 questions, choosing at least one from each section. Find the number of ways in which the candidate can choose the questions.
A. `""^(15)C_(5)`
B. `""^(3)C_(1)xx""^(12)C_(4)`
C. 2250
D. 2253

Answer 1

We observe that
Total number of ways of choosing at least one question from each section
= Total number of ways of choosing 5 questions out of 15 questions
- Number of ways of selecting 5 questions from 2 sections only
- Number of ways of choosing 5 questions from one section only.
`=""^(15)C_(5)-""^(3)C_(2)(""^10C_(5)-""^(2)C_(1)xx""^(5)C_(5))-""^(3)C_(1)xx""^(5)C_(5)`
`=""^(15)C_(5)-3xx""^(10)C_(5)+6-3=2250`