Key Concepts

• According to the Addition Principle, if one event can occur in [latex]m[/latex] ways and a second event with no common outcomes can occur in [latex]n[/latex] ways, then the first or second event can occur in [latex]m+n[/latex] ways.
• According to the Multiplication Principle, if one event can occur in [latex]m[/latex] ways and a second event can occur in [latex]n[/latex] ways after the first event has occurred, then the two events can occur in [latex]m\times n[/latex] ways. This is also known as the Fundamental Counting Principle.
• To determine how many permutations there are given [latex]n[/latex] 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.