Counting
In Probability,
| Counting Strategies | With Replacement | Without Replacement |
|---|---|---|
| With Ordering | $n^k$ | $n! \over (n-1)!$ |
| Without Ordering | $(n-1+k)! \over {(n-1)! ~k!}$ | $n! \over {(n-1)!~k!}$ |
In Probability,
| Counting Strategies | With Replacement | Without Replacement |
|---|---|---|
| With Ordering | $n^k$ | $n! \over (n-1)!$ |
| Without Ordering | $(n-1+k)! \over {(n-1)! ~k!}$ | $n! \over {(n-1)!~k!}$ |