Counting Principles

Master the addition and multiplication principles of counting.

The Addition Principle

If a task can be done in m ways and another task in n ways, and the two tasks cannot be done at the same time, then there are m + n ways to do one of the tasks.

Example:
  A restaurant offers 3 appetizers and 5 main courses.
  Number of ways to choose an appetizer OR a main course: 3 + 5 = 8

The Multiplication Principle

If a task consists of two stages, the first can be done in m ways and the second in n ways (independently), then the total number of ways is m × n.

Example:
  A restaurant offers 3 appetizers and 5 main courses.
  Number of ways to choose BOTH an appetizer AND a main course: 3 × 5 = 15

  A lock has 3 dials with 10 digits each.
  Total combinations: 10 × 10 × 10 = 1000

When to Use Which

Use ADDITION when:
  "OR" — choosing one option from multiple alternatives
  Tasks are mutually exclusive

Use MULTIPLICATION when:
  "AND" — performing multiple tasks in sequence
  Tasks are independent

🧪 Quick Quiz

The multiplication principle states that if task A can be done in m ways and task B in n ways, then both can be done in:

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