Key Concepts

• According to the Addition Principle, if one event can occur in $m$ ways and a second event with no common outcomes can occur in $n$ ways, then the first or second event can occur in $m+n$ ways.
• According to the Multiplication Principle, if one event can occur in $m$ ways and a second event can occur in $n$ ways after the first event has occurred, then the two events can occur in $m\times n$ ways. This is also known as the Fundamental Counting Principle.
• To determine how many permutations there are given $n$ distinct options,
  • Determine how many options there are for the first situation.
  • Determine how many options are left for the second situation.
  • Continue until all of the spots are filled.
  • Multiply the numbers together.