Question

How many ways can a team of 22 hockey players choose a captain and two alternate captains?

Answer 1

There are 9,240 distinct ways to choose a captain and two alternate captains from a team of 22 hockey players, by calculating 22 × 21 × 20.

Step-by-step explanation:

The question is about determining the number of ways to choose a captain and two alternate captains from a team of 22 hockey players. This problem can be solved using combinatorics, specifically the concept of permutations where order matters because the captain and alternate captains are distinct positions.

First, a captain is chosen out of the 22 players, which can be done in 22 ways. After choosing a captain, there are 21 players left to choose the first alternate captain, and that can be done in 21 ways. Finally, for the second alternate captain, 20 players are left, allowing for 20 ways to make this choice.

The total number of ways to choose the captain and the two alternate captains is the product of these distinct choices: 22 × 21 × 20. It is important to note that these positions are distinct, so the order in which we select the captain and alternate captains matters.

Therefore, the team has 22 × 21 × 20 = 9,240 distinct ways to choose a captain and two alternate captains.

Answer 2

you can write down 22 names but them in a box and there is a 1 out of 22 percent chance that each player will pick once