To cast the play with 6 volunteers into 3 characters, you would use a combination, specifically selecting 3 volunteers out of 6.
The formula for combinations is:
C(n, k) = n! / (k!(n - k)!)
Where:
- n is the total number of volunteers (6 in this case).
- k is the number of characters (3 in this case).
- ! denotes factorial.
Substituting the values into the formula:
C(6, 3) = 6! / (3! * (6 - 3)!)
Solving this:
C(6, 3) = (6! / (3! * 3!)) = (6*5*4) / (3*2*1) = 20
So, there are 20 ways to cast the play with 3 characters out of 6 volunteers.
