Choosing with repetition

#stars and bars#repetition#combinations

Statement

How many ways can we choose $3$ items from $5$ types with repetition allowed?

Hint

$\binom{3+5-1}{3}=\binom{7}{3}$ .

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Formula. $\binom{n+k-1}{k}$ with $n=5$ types, $k=3$ items: $\binom{7}{3}=35$ .

Conclusion. There are $35$ multisets of size $3$ from a $5$ -set.