Everyone Loves Cupcakes

Discrete Mathematics Level 4

It's Alice's birthday and she invites 9 of her best friends over for her birthday party. Alice and her friends are all having a great time when Alice's dad brings out a tray of cupcakes. There are 10 cupcakes on the tray, one for each kid at the party. Everyone lines up anxiously awaiting to get a cupcake, and one by one each kid takes a cupcake from the tray.

Unfortunately, some of Alice's friends are greedy! They take more than their fair share of cupcakes, and Alice, who's last in line, doesn't get one! How many ways could this have happened? In other words, how many ways could we arrange 9 numbers such that their sum is 10?

Details and Assumptions

  • Alice's friends could have taken anywhere from 0 cupcakes to all 10 cupcakes.

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