## Counting Possible Outcomes

Counting is the basis of any probability as we must first identify the number possible outcomes, as well as the number of desirable outcomes.

**Ordered Sets, With Replacement:**In this case, the same element can reappear multiple times.**Ordered Sets, Without Replacement:**In the ordering of 2 elements, A and B, AB and BA are distinct. AA or BB is not allowed. $outcomes=\frac{N!}{(N-n)!}$**Unordered Sets, Without Replacement (N choose n):**In the ordering of 2 elements, A and B, AB = BA, but AA or BB is not allowed. $outcomes=_NC_n=\Big( ^N_n \Big)=\frac{N!}{n!(N-n)!}$**Permutations**: How many different ways to order a set of objects: $outcomes=P_N=N!$

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