The Counting Principle

Grade 7 Math Worksheets

The Counting Principle, or Multiplication Principle, is a fundamental rule in combinatorics used to count the number of possible outcomes in a sequence of events.

Table of Contents:

The Counting Principle
Example of the Counting Principle
Formulae of Counting Principle
FAQs

Personalized Online Tutoring

The Counting Principle - Grade 7 Math Worksheet PDF

This is a free worksheet with practice problems and answers. You can also work on it online.

Solve Worksheet

"We really love eTutorWorld!"

"We really love etutorworld!. Anand S and Pooja are excellent math teachers and are quick to respond with requests to tutor on any math topic!" - Kieran Y (via TrustSpot.io)

View 7th Grade Online Tutoring Services

"My daughter gets distracted easily"

"My daughter gets distracted very easily and Ms. Medini and other teachers were patient with her and redirected her back to the courses.

With the help of Etutorworld, my daughter has been now selected in the Gifted and Talented Program for the school district"

- Nivea Sharma (via TrustSpot.io)

Book a Free Class

The Counting Principle

The counting principle, or multiplication principle, is a fundamental rule in combinatorics used to count the number of possible outcomes in a sequence of events. It states that if m ways to perform one event and n ways to perform another after the first event, then there are m x n ways to perform both events together.

For example, consider a person who has 3 shirts and 4 pants. The multiplication principle gives the total number of ways to choose one shirt and pair of pants: 3 x 4 = 12. Therefore, 12 different outfits can be created using these shirts and pants.

The multiplication principle can be extended to more than two events. For instance, if m ways to perform the first event, n ways to perform the second event, and p ways to perform the third event, then there are m x n x p ways to perform all three events together.

The multiplication principle is an essential concept in probability theory, as it is often used to count the number of possible outcomes in a sample space. It can also be used in other areas of mathematics and science, such as computer science, physics, and economics.

Example of the Counting Principle

Here’s an example of the counting principle:

Suppose you have 4 shirts and 3 pairs of pants. How many different outfits can you create using one shirt and one pant?

Using the counting principle, we multiply the number of ways to choose a shirt (4) by the number of ways to choose a pant (3):

4 x 3 = 12

Therefore, 12 different outfits can be created using these shirts and pants. These outfits are:

Shirt 1 and Pant 1
Shirt 1 and Pant 2
Shirt 1 and Pant 3
Shirt 2 and Pant 1
Shirt 2 and Pant 2
Shirt 2 and Pant 3
Shirt 3 and Pant 1
Shirt 3 and Pant 2
Shirt 3 and Pant 3
Shirt 4 and Pant 1
Shirt 4 and Pant 2
Shirt 4 and Pant 3

So, using the counting principle, we can see that there are 12 different outfits that can be created by choosing one shirt and one pant.

“There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.

Our kid is doing much better with a higher score.”

- Meg, Parent (via TrustSpot.io)

7th Grade Tutoring

eTutorWorld offers Personalized Online Tutoring for Math, Science, English, and Standardised Tests.

Our Tutoring Packs start at just under $22.49 per hour, and come with a moneyback guarantee.

Schedule a FREE Trial Session, and experience quality tutoring for yourself. (No credit card required.)

Book a Free Class

Formulae of the Counting Principle

The formula for the counting principle, also known as the multiplication principle, is:

Formula for the Counting Principle

If there are m ways to perform one event and n ways to perform another event after the first event, then there are m x n ways to perform both events together.

This can be extended to more than two events:

If there are m ways to perform the first event, n ways to perform the second event, and p ways to perform the third event, then there are m x n x p ways to perform all three events together.

In general, if there are k events, with the i-th event having mi possible outcomes, then the total number of possible outcomes is given by:

m1 x m2 x … x mk

This formula can be used to count the number of possible outcomes in a variety of situations, such as arranging objects in a specific order, selecting a subset of objects from a larger set, or choosing objects with or without replacement.

Do You Stack Up Against the Best?

If you have 30 minutes, try our free diagnostics test and assess your skills.

Free Diagnostic Test for 7th Grade

The Counting Principle FAQS

What is the counting principle?

The counting principle is a fundamental rule in combinatorics that is used to count the number of possible outcomes in a sequence of events. It states that if there are m ways to perform one event and n ways to perform another event after the first event, then there are m x n ways to perform both events together.

What is the multiplication principle?

The multiplication principle is another name for the counting principle. It refers to the idea that the number of ways to perform a sequence of events is equal to the product of the number of ways to perform each individual event.

When is the counting principle used?

The counting principle is used whenever you need to count the number of possible outcomes in a sequence of events. It is particularly useful in probability theory, as it allows you to calculate the probability of a particular event occurring.

How do you apply the counting principle?

To apply the counting principle, you need to identify the number of ways that each event can occur, and then multiply these numbers together. If there are more than two events, you can continue multiplying the numbers together for each additional event.

What are some examples of using the counting principle?

Examples of using the counting principle include counting the number of possible outcomes in a coin toss, the number of possible combinations of items in a menu, or the number of possible arrangements of letters in a word.

Can the counting principle be used for infinite sequences of events?

No, the counting principle cannot be used for infinite sequences of events. It only applies to finite sequences, where the number of possible outcomes is countable.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

Affordable Tutoring Now Starts at Just $22.49

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12. We are also a leading provider of Test Prep help for Standardized Tests (SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE, and AP).

What makes eTutorWorld stand apart are: flexibility in lesson scheduling, quality of hand-picked tutors, assignment of tutors based on academic counseling and diagnostic tests of each student, and our 100% money-back guarantee.

Whether you have never tried personalized online tutoring before or are looking for better tutors and flexibility at an affordable price point, schedule a FREE TRIAL Session with us today.

*There is no purchase obligation or credit card requirement

Book a Free Class