Nondecreasing uniform samples
= Nondecreasing uniform samples
{title2=$P(X_1\leq\cdots\leq X_r)=\binom{n+r-1}{r}/n^r$}
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.