I have been trying to solve this problem(I haven't taken it from any textbook so I don't know if there can be found any solution). Here is the problem: Supposing that we have a set $S=\{\alpha_1,\alpha_2,\alpha_3,...,\alpha_n\}$ and we want to collect from that set $S$ say $m$ items(we can collect one item more than once and we can even not collect another one. The question is for a given $m$ how many different collections of items can we get? (a different composition each time)(Can we find a formula expressed using the number of the items of $S$, $n$ and the number of items we want to collect: $m$ ?)
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I want to make sure I understand your question. Say $S={a,b,c}$ and $m=3$. Can you confirm that the set of things you are counting is$$aaa,aab,aac,abb,abc,acc,bbb,bbc,bcc,ccc?$$ – Mike Earnest Jul 18 '22 at 15:03
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@MikeEarnest That is what I am looking for. – Kani Pen Jul 18 '22 at 15:04