Question

In how many ways can a group of 5 men and 2 women be made out of total of 7 men and 3 women?

• A. 63
• B. 45
• C. 126
• D. 90
• E. None of these

Answer 1

The correct option is A 63

There are 7 men and 3 women. We have to select 5 men out of 7 and 2 women out of 3.
This can be done is ${}^7{C}_5{\times }^3{C}_2$ ways.
$\therefore$ The number of ways of making the selection
${=}^7{C}_5{\times }^3{C}_2=\frac{7\times 6}{1\times 2}\times \frac{3\times 2}{1\times 2}=63$