COUNTING PRINCIPLE

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 S 1, S 2, and S 3 and two T-shirts T 1, T 2. Then the possible ways she can choose her dress are:
S 1, T 1
S 1, T 2
S 2, T 1
S 2, T 2
S 3, T 1
S 3, T 2
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.

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.

Quick Summary

The counting principle helps determine the total number of outcomes when multiple events occur.
Multiply the number of possibilities for each independent event to find the total number of possible outcomes.

\[ N = n_1 \times n_2 \times ... \times n_k \]

🍎 Teacher Insights

Use real-world examples like choosing outfits or creating passwords to illustrate the principle. Emphasize the importance of independence between events.

🎓 Prerequisites

Basic Arithmetic
Multiplication

Check Your Knowledge

Q1: A restaurant offers 5 appetizers, 10 main courses, and 4 desserts. How many different meals consisting of one appetizer, one main course, and one dessert are possible?

20 40 200 600

Q2: How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if repetition of digits is allowed?

15 125 60 243

Frequently Asked Questions

Q: When do I use the counting principle?
A: Use it when you need to find the total number of ways multiple independent events can occur.

Q: What if the events are not independent?
A: The counting principle does not directly apply. You may need to use conditional probability or other counting techniques.