Counting Techniques

The Fundamental Rule of Counting (the mn Rule);

Permutations; andCombinations

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 = Pnx = (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 = Cnx = (n!) / x!(n - x)!