f r-multisetsI assume that $r$-multisets means multisets of cardinality $r$, and by combining zeros and ones the problem means arranging them in a row. The number of multisets of cardinality $r$ consisting of $n$ distinct objects equals the number of tuples $(r_1,\dots,r_n)$ such that $r_i\ge0$ for all $i$ and $\sum_{i=1}^n r_i=r$. Here $r_i$ serves as the number of copies of object number $i$. In turn, arranging $r$ zeros in a row and inserting $n-1$ ones between them amounts to dividing zeros into $n$ groups, some of which may be empty. Thus, each arrangement gives rise to a tuple described above.mathmaniac said:
f r-multisets