Counting Techniques

1
Counting Techniques

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

2
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.

3
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)!

4
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)!