# 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.

**Q1: **

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

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**Q2: **

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

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**Q3: **

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?

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**Q4: **

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.

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**Q5: **

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.

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**Q6: **

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?

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**Q7: **

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?

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**Q8: **

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.

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**Q9: **

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?

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**Q10: **

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?

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