Answer: 4950 ways
Explanation:
Given : Number of roles for men = 2
Number of roles for women = 4
We know that the combination of n things taken r at a time is given by :-

Then, If five men and 12 women try out for these parts then the number of different ways can the director choose people for the roles :-

Hence, the director can choose people for the roles in 4950 ways .