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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: $outcomes=P_N=N!$
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