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.

Video Examples: The Counting Principle

Example 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:
    S1, T1
    S1, T2
    S2, T1
    S2, T2
    S3, T1
    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

Ques: Using the counting principle, find the number of possible combinations/choices if there are 3 shirts, 7 skirts and 8 pairs of shoes.

    A. 168
    B. 18
    C. 80
    D. 45
    Correct Answer: A


    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.

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