counting principle


Definition of Counting Principle

  • Counting Principle is used to find the number of possible outcomes. It states that if an event has m possible outcomes and another independent event has n possible outcomes, then there are mn possible outcomes for the two events together.

Examples of Counting Principle

  • Sandra has three skirts S1, S2, and S3 and two T-shirts T1, T2. Then the possible ways she can choose her dress are:
    1. S1, T1
    2. S1, T2
    3. S2, T1
    4. S2, T2
    5. S3, T1
    6. S3, T2
    There are 6 distinct possible ways of Sandra choosing her dress. This can easily be calculated using the counting principle as 3 × 2 = 6.

Solved Example on Counting Principle

Using the counting principle, find the number of possible combinations/choices if there are 3 shirts, 7 skirts and 8 pairs of shoes.
Choices:
A. 168
B. 18
C. 80
D. 45
Correct Answer: A
Solution:
Step 1: Number of outcomes of picking a shirt from 3 shirts is 3.
Step 2: Number of outcomes of picking a skirt from 7 skirts is 7.
Step 3: Number of outcomes of picking a pair of shoes from 8 pairs is 8.
Step 4: So, the number of possible combinations/choices in the given situation is 3 × 7 × 8 = 168.

Related Terms for Counting Principle

  • Outcomes
  • Independent Event
  • Permutation