The Counting Principle

The basic counting principle states that if there are X ways to do one thing, and Y ways to do another, then there are X × Y ways of doing both.

Similarly, if there are X ways to do one thing, and Y ways to do second one and Z ways to do third one, then there are X × Y × Z ways of doing all the three.

Example: There are 6 pink kites and 4 yellow kites. Daniel wants to choose 2 kites – 1 pink and the other of yellow color. In how many ways can Daniel choose the kites?

The Counting Principle states that we multiply the number of choices to find the total number of possibilities.

So, number of ways Daniel can choose the kites = 6 × 4 = 24 ways

Example: Isabelle wants to order frozen yoghurt. If there are 5 different flavours of yoghurt and 14 different toppings to choose from, then in how many different ways can Isabelle place her order?

Number of ways Isabelle can place her order = 5 × 14 = 70 ways


Check Point

  1. Sandy wants to buy flowers for his friend. There are 5 colors of roses, 4 colors of lilies, and 2 types of orchids. In how many ways can Sandy choose 3 flowers of each type?
  2. A kitchen garden shop has 6 types of floral plants and 12 plants of different vegetables. Hebrew wants to buy one floral plant and one plant from vegetables. In how many ways can he choose the 2 plants?
  3. Shawna’s doll has 6 different dresses, 5 sandals and 4 colors of hairs, which are detachable and can be replaced. In how many ways can Shawna dress up her doll?
  4. Millie’s grandmother bought 2 types of bread and made 4 types of fillings for sandwiches. In how many different ways can her grandmother make sandwiches?
  5. Peter has 6 shirts, 3 neck ties and 4 trousers for a party. In how many ways can he dress up himself?
Answer key
  1. 40 ways
  2. 72 ways
  3. 120 ways
  4. 8 ways
  5. 72 ways

Download/Solve a Worksheet for The Counting Principle

Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?

© 2020 eTutorWorld - Online Tutoring and Test Prep | All rights reserved

Stay Safe, Learn at Home from Personalized Online Tutors


Use Coupon

SAFE10 to save 10% on Learning Packs *

TEST20 to save 20% on Test Prep Worksheets


* Max. discount for learning packs is $50

You have Successfully Subscribed!