Question

From a group of 7 boys and 6 girls, 5 students are to be selected to form a committee so that at least 3 boys are there on the committee. In how many ways can it be done?

• A. 570
• B. 659
• C. 756
• D. 840

Answer 1

The correct option is C 756

We may have ( 3 boys and 2 girls) or (4 boys and 1 girl) or (5 boys only)
Therefore, Required number of ways =
$={(}^7{C}_3{\times }^6{C}_2)+{(}^7{C}_4{\times }^6{C}_1){+}^7{C}_5=(\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{6\times 5}{2\times 1})+\left({}^7{C}_3{\times }^6{C}_1\right)+{}^7{C}_2=525+210+21=756$