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Question
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
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Solution
There are 11 questions, out of which 5 questions are from section I and 6 questions are from section II.
The student has to select 6 questions taking at least 2 questions from each section.
Consider the following table:
| Case I | Case II | Case III | |
| No. of questions | Sec I (2Q) Sec II (4Q) |
Sec I (3Q) Sec II (3Q) |
Sec I (4Q) Sec II (2Q) |
| Number of ways | 5C2 × 6C4 = 10 × 15 = 150 |
5C3 × 6C3 = 10 × 20 = 200 |
5C4 × 6C2 = 5 × 15 = 75 |
∴ Number of choices = 150 + 200 + 75 = 425
∴ In 425 ways students can select 6 questions, taking at least 2 questions from each section.
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