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?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Required number of ways}} \cr & = {{}^7{C_5} \times {}^3{C_2}} \cr & = {{}^7{C_2} \times {}^3{C_1}} \cr & = {\frac{{7 \times 6}}{{2 \times 1}} \times 3} \cr & = 63 \cr} $$