Question

A candidate is required to answer 6 out of 12 questions which are divided into two parts \(A\) and \(B\), each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she make up his/her choice of 6 questions ?
(A) 850
(B) 800
(C) 750
(D) 700

Answer 1

Ans : (A)
Hint: A B
$$
\begin{aligned}
42 & \rightarrow{ }^{6} \mathrm{C}_{4} \times{ }^{6} \mathrm{C}_{2} \\
24 & \rightarrow{ }^{6} \mathrm{C}_{2} \times{ }^{6} \mathrm{C}_{4} \\
33 & \rightarrow{ }^{6} \mathrm{C}_{3} \times{ }^{6} \mathrm{C}_{3} \\
\text { Total } &=2 \times{ }^{6} \mathrm{C}_{2} \times{ }^{6} \mathrm{C}_{4} \times{ }^{6} \mathrm{C}_{3} \times{ }^{6} \mathrm{C}_{3}=450+400=850
\end{aligned}
$$