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State whether the question is a Permutation or a Combination, then solve. The ski club has ten members to choose two co-captains. How many ways can these positions be filled?

User Nomi Ali
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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.

User Daniel Olszewski
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