Answer: 4950 ways
Step-by-step 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 :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
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 :-
[tex]^5C_2\times ^{12}C_4=\dfrac{5!}{2!(5-2)!}\times\dfrac{12!}{4!(12-4)!}\\\\=10\times495=4950[/tex]
Hence, the director can choose people for the roles in 4950 ways .
