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Question
A student has to answer 10 questions, choosing at least 4 from each of part A and part 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 various possibilities for answering the 10 questions are given below:
(i) 4 from part A and 6 from part B.
(ii) 5 from part A and 5 from part B.
(iii) 6 from part A and 4 from part B.
∴ Required number of ways =\[{}^6 C_4 \times^7 C_6 + {}^6 C_5 \times^7 C_5 + {}^6 C_6 \times^7 C_4\]
\[= \frac{6!}{4! 2!} \times 7 + 6 \times \frac{7!}{5! 2!} + 1 \times \frac{7!}{4! 3!} \]
\[ = 105 + 126 + 35\]
\[ = 266\]
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