Genre 6: Annotated Story Problem

Jane is going to Cedar Point on Friday. Five of her friends want to go, however, she only has room in her car for three. To be fair, she will choose the three that will go with her randomly. Using Pascal's triangle find how many possible ways her friends can go with her (order does not matter).
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Since order does not matter we can use a combination to find the number of ways. She is choosing 3 friends from a group of 5. We can write this in the notation 5 Choose 3. At this point we could either use a formula, or write out all the possible combinations, however, we will use Pascal's triangle to help us.

First, since we are choosing from 5, we will go down to row number 5 (the top row is not counted).

Next, since we are choosing 3, we will count three columns to the right (starting on 5, the first column is not counted)

We can see that this gives us 10. Therefore, there are 10 different combinations of friends she can take to Cedar Point.