On a skiing trip, there are five people but only three pairs of skis. How many different groups of three could ski?

The question pertains to combinatorics, a branch of mathematics dealing with combinations and permutations. Since it involves deciding how many different groups of three can be made with five people sharing three pairs of skis, it's an application of combinatorial mathematics.
To solve this problem, you can use the combination formula, which is used when you want to find out how many ways you can choose k items from a larger set of n items, and the order of selection does not matter. The combination formula is given as:
C(n, k) = n! / (k! (n - k)!).
Here, we want to find the number of groups of three that can be formed from five people, so we will calculate C(5, 3):
C(5, 3) = 5! / (3! (5 - 3)!) = (5 x 4 x 3 x 2 x 1) / ((3 x 2 x 1) (2 x 1)) = 10.
Therefore, there are 10 different groups of three that could ski from the group of five people.

Answered by JunoTemple | 2024-06-18

So let's start by naming our people, let's say Robert, Sasha, Tyler, Bryan, and Katie. Now start listing all the ways that they can go in a organized way. Robert, Sasha, Tyler Robert, Sasha, Bryan Robert, Sasha, Katie Robert, Tyler, Bryan Robert, Tyler, Katie Robert, Bryan, Katie Sasha, Tyler, Bryan Sasha, Tyler, Katie Tyler, Bryan, Katie And that is it, 9, without repeating the same groups

Answered by theapplezoo | 2024-06-24

There are a total of 10 different groups of three people that can ski from a group of five. This is calculated using the combination formula. The combination formula allows us to choose items without caring about the order of selection.
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Answered by theapplezoo | 2024-09-03