Final answer:
To find the number of possible sets for the positions of captain, co-captain, and towel runner, we need to use permutations. In this case, the number of possible sets is 13,800.
Step-by-step explanation:
To find the number of possible sets for the positions of captain, co-captain, and towel runner, we can use the concept of permutations. Permutations are used when the order of items matters. In this case, the order of selection for the positions matters, so we need to use permutations to calculate the number of possible sets.
The number of possible sets can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
In this problem, we have 25 teammates and need to select 3 positions, so the number of possible sets is:
P(25, 3) = 25! / (25 - 3)!
Simplifying the expression:
P(25, 3) = 25! / 22!
25! = 25 x 24 x 23
22! = 22 x 21 x 20 x ... x 1
Simplifying further:
P(25, 3) = (25 x 24 x 23) / (20 x 19 x 18)
P(25, 3) = 13,800
Therefore, there are 13,800 possible sets for the positions of captain, co-captain, and towel runner.