Final answer:
To find the different ways the show choir can be formed, we can use the combination formula. In this case, we have 40 students trying out for 12 spots, so the combination is C(40, 12) which is approximately 39,087,164.
Step-by-step explanation:
To find the number of different ways the show choir can be formed, we can use the concept of combinations. In this case, we have 40 students trying out for 12 spots, so we can use the combination formula.
The combination formula is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items chosen. In this case, n = 40 and r = 12.
Plugging the values into the formula, we get:
C(40, 12) = 40! / (12!(40-12)!) = 40! / (12!28!)
Simplifying further:
C(40, 12) = (40 * 39 * 38 * ... * 29 * 28!)/(12 * 11 * 10 * ... * 1 * 28!)
Canceling out the common terms in the numerator and denominator, we get:
C(40, 12) = (40 * 39 * 38 * ... * 29) / (12 * 11 * 10 * ... * 1)
Calculating this expression using a calculator or software, we find that C(40, 12) is approximately 39,087,164.