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 ?

• A. $266$
• B. $260$
• C. $256$
• D. $270$

Answer 1

Answer: (A)

$266$

Answer 2

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 $= \,^{6}C_{4} \times ^{7}C_{6} \times ^{6}C_{5} \times ^{7}C_{5} \times^{6}C_{6} \times ^{7}C_{4}$ $= 105 + 126 + 35$ $=266$.