Twenty girls are trying out for the cheer squad. How many different 12 girl teams can be made?
C(20,12) = 125,970
To find the number of different 12-girl teams that can be made from a group of 20 girls, we need to use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n - r)!)
Where n is the total number of girls and r is the number of girls we want to select for the team.
In this case, n = 20 (total number of girls) and r = 12 (number of girls we want to select for the team).
Plugging the values into the formula:
C(20, 12) = 20! / (12!(20 - 12)!)
Calculating the factorial values:
20! = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
(20 - 12)! = 8!
Simplifying the equation:
C(20, 12) = (20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) x (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1))
After simplifying, most of the terms in the numerator and denominator will cancel out:
C(20, 12) = (20 x 19 x 18 x 17 x 16 x 15 x 14 x 13) / (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
Evaluating the remaining values:
C(20, 12) = 3,838,380
Therefore, there are 3,838,380 different 12-girl teams that can be made from a group of 20 girls.