Answer:
To find the number of different cast lists, we can use the concept of combinations.
We need to select 4 males out of 6 available actors, which can be done in C(6, 4) ways. Here, C(n, r) represents the number of combinations of selecting r items from a set of n items.
Similarly, we need to select 3 females out of 8 available actresses, which can be done in C(8, 3) ways.
To find the total number of different cast lists, we multiply these two combinations together:
Total number of cast lists = C(6, 4) * C(8, 3)
Now, let's calculate these combinations:
C(6, 4) = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5 * 4!) / (4! * 2 * 1) = 15
C(8, 3) = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6!) / (3! * 3 * 2 * 1) = 56
Therefore, the total number of different cast lists is:
Total number of cast lists = 15 * 56 = 840
So, there are 840 different cast lists possible for this play.
