Final answer:
This is a permutation problem where the order of selection matters. There are 90 different ways to choose two co-captains from the ten members of the ski club.
Step-by-step explanation:
The question asks about selecting two co-captains from a ski club with ten members. This is a permutation problem because the order in which the co-captains are selected matters, with one being the first co-captain and the other being the second co-captain.
To solve this, we use the formula for permutations, which is P(n, r) = n! / (n-r)! Here, n is the total number of items to choose from, and r is the number of items to choose. In our case, n is 10 and r is 2.
P(10, 2) = 10! / (10-2)!
P(10, 2) = 10! / 8!
= (10 x 9 x 8!) / 8!
= 10 x 9
= 90. There are 90 different ways the two co-captain positions can be filled.