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)

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