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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? - Mathematics

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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 =\[{}^6 C_4 \times^7 C_6 + {}^6 C_5 \times^7 C_5 + {}^6 C_6 \times^7 C_4\]

\[= \frac{6!}{4! 2!} \times 7 + 6 \times \frac{7!}{5! 2!} + 1 \times \frac{7!}{4! 3!} \]
\[ = 105 + 126 + 35\]
\[ = 266\]

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 11 | Page 16

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