Nondecreasing uniform samples ($P(X_1\le \cdots \le X_r)=\left(\genfrac{}{}{0ex}{}{n+r-1}{r}\right)/n^r$)

An ordered sample from $n$ equally likely values is nondecreasing exactly when it is the unique sorted representative of its multiplicities. Stars and bars counts the nonnegative multiplicities summing to $r$; repeated values are included automatically.