Question

From a group of 7 men and 6 women 5 people are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways an it be done?

• A. 756
• B. 735
• C. 564
• D. 645

Answer 1

The correct option is A 756

${}^7{C}_3{\times }^6{C}_2{+}^7{C}_4{\times }^6{C}_1{+}^7{C}_5{\times }^6{C}_0$

${}^7{C}_3{\times }^6{C}_2{+}^7{C}_3\times 6{+}^7{C}_2\times 1$

$\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{6\times 5}{2\times 1}+\frac{7\times 6\times 5}{3\times 2\times 1}\times 6+\frac{7\times 6}{2\times 1}$

$525+210+21=756.$