6 hockey players want to be either a captain or an assistant. The 1st player chosen will be the captain, and the second will be the assistant.
How many ways can these players be chosen captain and assistant?
Is this a permutation or a combination?
Please help!!
Thank you.
To determine the number of ways these 6 hockey players can be chosen as captain and assistant, we need to consider the order in which they are chosen. Since the first player chosen will be the captain and the second will be the assistant, we are dealing with permutations.
To calculate the number of permutations, we can use the formula for calculating permutations of n objects taken r at a time, which is given by:
P(n, r) = n! / (n - r)!
In this problem, we have 6 players and we want to choose 2 of them to be the captain and assistant. So, n = 6 and r = 2. Plugging these values into the formula, we get:
P(6, 2) = 6! / (6 - 2)!
= 6! / 4!
= (6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1)
= 6 * 5
= 30
Therefore, there are 30 ways to choose the captain and assistant from the 6 hockey players.
To summarize, this is a permutation problem since we are concerned with the order in which the players are chosen. The number of ways can be calculated using the permutation formula, P(n, r) = n! / (n - r)!. In this case, there are 30 ways to choose the captain and assistant.