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Question
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
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Solution
The possibilities are: 4 from Part A and 6 from Part B
or 5 from Part A and 5 from Part B
or 6 from Part A and 4 from Part B.
Therefore, the required number of ways is
6C4 × 7C6 + 6C5 × 7C5 + 6C6 × 7C4
= 105 + 126 + 35
= 266.
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