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.
There are 6 ways to choose a captain, and 5 from the remaining players as a assistant.
So there is a total of 6*5=30 ways.
It is a permutation because the order of choice matters.
To determine the number of ways the players can be chosen as captain and assistant, we need to determine whether this is a permutation or a combination problem.
Permutations are used when the order of selection matters, meaning that different orders would yield different outcomes. Combinations, on the other hand, are used when the order of selection does not matter.
In this case, the order of selection does matter because being chosen as the captain is different from being chosen as the assistant. Therefore, we can conclude that this is a permutation problem.
To find the number of permutations in this scenario, we can use the formula for calculating permutations, which is:
P(n, r) = n! / (n - r)!
where n is the total number of items, and r is the number of items being chosen.
In this case, we have 6 hockey players who can be chosen as captain and assistant, so n = 6 and r = 2.
Using the formula, we can calculate the number of permutations:
P(6, 2) = 6! / (6 - 2)!
= 6! / 4!
= (6 x 5 x 4!) / 4!
= (6 x 5)
= 30
Therefore, there are 30 different ways the players can be chosen as captain and assistant.