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4 votes
4 votes
We go to a pizza party, and there are $5$ types of pizza. We have been starving for days, so we can eat $13$ slices, but we want to sample each type at least once. In how many ways can we do this? Order does not matter.
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1 Answer

5 votes
5 votes
First, we sample the $5$ types. That leaves space for $8$ more, which we can choose freely, with repetition. The dots-and-bars(stars and bars) formula tells us that there are
$$
\left(\begin{array}{c}
8+5-1 \\
5-1
\end{array}\right)=\left(\begin{array}{c}
12 \\
4
\end{array}\right)
$$
ways to do this.
Answer:

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