In how many ways, can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 63
The order in which people are chosen does not matter, so each choice is a combination. The men and the women are chosen independently, so the two counts are multiplied.
5 men out of 7: \(^{7}C_{5}=\,^{7}C_{2}=\displaystyle\frac{7\times6}{2}=21\)
2 women out of 3: \(^{3}C_{2}=3\)
Number of groups: \(21\times3=\) 63