Questions: Combination or Permutation Question: a skating competition of 17 skaters, how many ways can you pick the best 2 skaters if you have to pick the exact order they place?

Solution Steps

To solve this problem, we need to determine the number of permutations of 2 skaters from a group of 17. Since the order in which the skaters are picked matters, we use permutations rather than combinations. The formula for permutations is given by \( P(n, r) = \frac{n!}{(n-r)!} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.

The problem requires finding the number of ways to select and order 2 skaters from a group of 17. Since the order matters, this is a permutation problem.

The formula for permutations is given by: \[ P(n, r) = \frac{n!}{(n-r)!} \] where \( n = 17 \) is the total number of skaters, and \( r = 2 \) is the number of skaters to be selected.

Substitute the values into the permutation formula: \[ P(17, 2) = \frac{17!}{(17-2)!} = \frac{17!}{15!} \] This simplifies to: \[ P(17, 2) = 17 \times 16 = 272 \]

Final Answer