# Probabilities and Statistics Formulaes Crib Sheet

## 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. $outcomes=N^n$
• 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: $outcomes=P_N=N!$