Question

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

• A. 266
• B. 5040
• C. 11760
• D. 86400
• E. None of these

Answer 1

The correct option is C 11760

Required number of ways $={(}^8{C}_5{\times }^{10}{C}_6)$
$={(}^8{C}_3{\times }^{10}{C}_4)$
$=\left(\begin{array}{c}\frac{8\times 7\times 6}{3\times 2\times 1}\times \frac{10\times 9\times 8\times 7}{4\times 3\times 2\times 1}\end{array}\right)$
$=11760.$