Stars and Bars

Formula

Stars and Bars is a combinatoric method of partitioning n items (stars) into k partitions, using k-1 partition-markers (bars).

This is an extremely useful formula, as it can help enumerate the number of ways of partitioning a group of items.

The number of ways of partitioning n objects into k partitions using k-1 bars is given by:

$ \binom{n+k-1}{k-1} $