Hey there! I'm happy to help!
When talking about possibilities of groups, outcomes, etc. we will either use permutations or combinations.
Permutations has to do with order.
Combinations does not have to do with order.
Our question says that the order in which the participants are chosen is irrelevant, so we will use combinations.
However, to get to combinations, you first have to find the permutation, which we will do below.
So, let's imagine that there are three seats you sit in to be in this group.
First, you have to pick someone to sit in the first chair. There are 17 choices to put in this chair.
For the second chair, you only have 16 choices because one of them is sitting in the first chair.
Following this, there are only 15 choices for the 3rd chair.
We multiply this number of choices together:
17×16×15=4080
Therefore, there are 4080 possible permutations here. This means ways you choose the people and how you order them.
Using our permutation, we will find the combination, where order does not matter.
To find the number of possible combinations, we have to divide our permutation by the number of possible ways you can arrange people in 3 seats. This will get rid of all of the extra possibilities with the same people but a different order.
How many ways can you arrange 3 people?
Well, there's 3 choices for the first seat, 2 for the second, and 1 for the third.
3×2×1=6
So, we divide 4080 by 6, giving us 680
Therefore, there are 680 groups of 3 participants that can be chosen assuming that the order in which the participants are chosen is irrelevant.
Have a wonderful day! :D
