Partitioning:
- Number of ways to partition n identical things in r distinct slots is given by: $$= ^{n+r-1} C_{r-1}$$
- Number of ways to partition n identical things in r distinct slots so that each slot gets at least 1: $$ = ^{n-1}C_{r-1}$$
- Number of ways to partition n distinct things in r distinct slots is given by: $$r^{n}$$
- Number of ways to partition n distinct things in r distinct slots where arrangement matters: $$\dfrac{(n+r-1)!}{(r-1)!}$$
