Search any question & find its solution
Question:
Answered & Verified by Expert
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 hisher choice of 6 questions?
Options:
Solution:
1641 Upvotes
Verified Answer
The correct answer is:
850
$$
\begin{array}{|c|c|}
\hline A & B \\
\hline 4 & 2 \\
\hline 3 & 3 \\
\hline 2 & 4 \\
\hline
\end{array}
$$
$\therefore$ Total number of ways $={ }^{6} C_{4} \times{ }^{6} C_{2}+{ }^{6} C_{3} \times{ }^{6} C_{3}+{ }^{6} C_{2} \times{ }^{6} C_{4}$
$=\frac{6 \times 5}{2 \times 1} \times \frac{6 \times 5}{2 \times 1}+\frac{6 \times 5 \times 4}{3 \times 2 \times 1} \times \frac{6 \times 5 \times 4}{3 \times 2 \times 1}+\frac{6 \times 5}{2 \times 1} \times \frac{6 \times 5}{2 \times 1}$
$=15 \times 15+20 \times 20+15 \times 15$
$=225+400+225$
$=850$
\begin{array}{|c|c|}
\hline A & B \\
\hline 4 & 2 \\
\hline 3 & 3 \\
\hline 2 & 4 \\
\hline
\end{array}
$$
$\therefore$ Total number of ways $={ }^{6} C_{4} \times{ }^{6} C_{2}+{ }^{6} C_{3} \times{ }^{6} C_{3}+{ }^{6} C_{2} \times{ }^{6} C_{4}$
$=\frac{6 \times 5}{2 \times 1} \times \frac{6 \times 5}{2 \times 1}+\frac{6 \times 5 \times 4}{3 \times 2 \times 1} \times \frac{6 \times 5 \times 4}{3 \times 2 \times 1}+\frac{6 \times 5}{2 \times 1} \times \frac{6 \times 5}{2 \times 1}$
$=15 \times 15+20 \times 20+15 \times 15$
$=225+400+225$
$=850$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.