Q77 / 180 · KCET 2021 · Mathematics

A student has to answer 10 questions, choosing at least 4 from each of the parts $A$ and $B$. If there are 6 questions in part $A$ and 7 in part $B$, then the number of ways can the student choose 10 questions is

  • A
    256
  • B
    352
  • Correct answer
    C
    266
  • D
    426

Solution

Given, Total number of questions in part $A=6$ Total number of questions in part $B=7$ Pattern to choose 10 questions from 13 questions is 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 $B$. $\therefore$ Total required number of ways $\begin{aligned} &=\left({ }^{6} C_{4} \times{ }^{7} C_{6}\right)+\left({ }^{6} C_{5} \times{ }^{7} C_{5}\right)+\left({ }^{6} C_{6} \times{ }^{7} C_{4}\right) \\ &=(15 \times 7)+(6 \times 21)+(1 \times 35) \\ &=105+126+35=266 \end{aligned}$

Hence, the correct answer is option: 'C'.

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