Answer:
30 different casts
Step-by-step explanation:
Involving the casting of a play in a community theater. Assume that there are 4 unfilled roles: 2 male and 2 female. There are 3 men and 5 women, including Jane, auditioning for a part in the play. How many different casts are there?
To find the number of different casts, find the number of ways the male and female are selected and multiply it together
We need to select 2 male from 3 men, use combination
Selecting 2 male from 3 men in 3C2 ways=[tex]\frac{3!}{2!(3-2)!} =3[/tex]
We need to select 2 female from 5 women, use combination
Selecting 2 female from 5 women in 5C2 ways=[tex]\frac{5!}{2!(5-2)!} =10[/tex]
3 times 10=30
So 30 different casts are there
