Counting Techniques The Fundamental Rule of Counting (the mn Rule); Permutations; and Combinations

The Fundamental Rule of Counting If event A can occur in m distinct ways and event B can occur in any of n distinct ways (regardless of how event A occurs), then event A and event B can occur in mn ways.

Permutations When different arrangements count as distinct outcomes but duplication of items is not allowed, then Permutations is the counting procedure for the arrangement of items. If there are n items and each item can occur x different ways, then Number of ways = P n x = (n!) / (n - x)!

Combinations When different arrangements do not count as distinct outcomes and duplication of items is not allowed, then Combinations is the counting procedure for the arrangement of items. If there are n items and each item can occur x different ways, then Number of ways = C n x = (n!) / x!(n - x)!