Lesson Worksheet: Counting Principles: Addition Rule Mathematics

In this worksheet, we will practice finding the number of all possible outcomes of 2 or more events together using the addition counting principle.


A certain action can be performed in 𝑚 different ways. A second action, which is mutually exclusive of the first, can be performed in 𝑛 different ways. Write an expression for the number of ways to perform either the first action or the second action.

  • A𝑚×𝑛
  • B𝑚𝑛
  • C𝑚
  • D𝑚+𝑛
  • E𝑚𝑛


How many ways can 2 pencils of the same color be selected from 6 red and 3 blue?

  • A𝐶𝐶
  • B𝑃+𝑃
  • C𝐶+𝐶
  • D𝐶×𝐶
  • E𝑃×𝑃


There are 10 boys and 6 girls. What is the numerical expression that allows us to calculate how many ways there are of forming a group that consists of either 3 boys or 2 girls?

  • A𝐶𝐶
  • B𝐶+𝐶
  • C𝐶×𝐶
  • D𝑃+𝑃
  • E𝑃×𝑃


In a final exam that consists of 12 questions, a quarter of them are essay questions and the rest are multiple-choice questions. A student has to solve 10 of the questions, where at least 7 of them are multiple-choice questions and the rest are essay questions. Write the calculation that would give the number of ways that the student can choose which questions to answer.

  • A𝐶×𝐶×𝐶×𝐶×𝐶×𝐶
  • B𝐶+𝐶+𝐶+𝐶+𝐶+𝐶
  • C𝐶×𝐶+𝐶×𝐶+𝐶×𝐶
  • D𝐶×𝐶+𝐶×𝐶+𝐶×𝐶
  • E𝐶+𝐶+𝐶×𝐶+𝐶+𝐶


Write the calculation we would use to work out the number of ways we can park 2 cars and then at least 2 trucks in 5 parking slots in a row.

  • A𝑃×𝑃+𝑃×𝑃
  • B𝐶+𝑃+𝑃+𝑃
  • C𝑃×𝑃+𝑃×𝑃
  • D𝐶×𝐶+𝐶×𝐶
  • E𝑃+𝑃+𝑃+𝑃


A cup contains 10 blue marbles, 6 green marbles, and 7 red marbles. None of the marbles in the cup are identical. How many ways can 4 marbles be chosen from the cup so that exactly 3 of them are the same color?

  • A13×𝑃+17×𝑃+16×𝑃
  • B𝑃+𝑃+𝑃
  • C𝐶+𝐶+𝐶
  • D𝐶×𝐶×𝐶
  • E13×𝐶+17×𝐶+16×𝐶


Which of the following expressions shows how to calculate the number of ways that a group of 6 people can be formed from 5 teachers and 10 parents, such that the group has at least one parent and at least 1 but fewer than 4 teachers?

  • A𝐶×𝐶+𝐶×𝐶+𝐶×𝐶
  • B𝐶×𝐶×𝐶×𝐶×𝐶×𝐶
  • C𝐶×𝐶+𝐶×𝐶+𝐶×𝐶+𝐶×𝐶
  • D𝐶+𝐶+𝐶+𝐶+𝐶+𝐶+𝐶+𝐶
  • E𝐶+𝐶+𝐶+𝐶+𝐶+𝐶


What is the numerical expression we would use to find in how many ways can 4 balls of the same color be selected from 10 blue balls, 6 green balls, and 7 red balls? Assume none of the balls are identical.

  • A𝐶×𝐶+𝐶
  • B𝐶×𝐶×𝐶
  • C𝑃×𝑃×𝑃
  • D𝐶+𝐶+𝐶
  • E𝑃+𝑃+𝑃


What is the numerical expression that allows us to calculate in how many ways can a group of 10 people be formed from 10 boys and 12 girls such that the group has at least 8 girls?

  • A𝐶+𝐶×𝐶+𝐶×𝐶
  • B𝐶×𝐶+𝐶×𝐶
  • C𝐶×𝐶+𝐶×𝐶
  • D𝐶×𝐶×𝐶×𝐶×𝐶
  • E𝐶×𝐶+𝐶×𝐶+𝐶


Michael is buying some stationery supplies for his office. He needs to buy 6 items, choosing from 20 types of pens, 10 types of pencils, and 5 types of printing paper. He must have at least 3 pens and only one paper package. Which of the following calculations represents the number of options Michael has when buying supplies?

  • A𝐶+𝐶+5+𝐶+10+5+𝐶+5
  • B𝐶+𝐶+5+𝐶+10+5+𝐶
  • C𝐶×𝐶+𝐶×10+𝐶
  • D𝐶×𝐶×5+𝐶×10×5+𝐶×5
  • E𝐶×𝐶×5+𝐶×10×5+𝐶

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