if i want to find the total number of ways of distributing a number of P identical things to a number of distinguishable N things, where ($p_{1}, p_{2}$,...,$p_{N}$)≠ ($p_{2}, p_{1}$,...,$p_{N}$), and $\sum p_{i}=P$, then it is a permutation since the order matter here, right? and the following will be the formula for calculating the total number of ways $$\frac{(P+N-1)!}{(P)!(N-1)!}$$ Is that right?
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2the answer there points to a link which i believe answered my question, thanks! – Jack Apr 09 '23 at 05:46