Use the Fundamental Counting Principle to solve Exercises 29–40.
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Question

Use the Fundamental Counting Principle to solve Exercises 29–40.

The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?

Accepted Answer

Hello. Today we're going to be using the fundamental counting principle to solve the following problem. We are told that a meal has five choices for the main dish and four choices for the beverage. We want to determine how many ways the meal can be ordered. So the fundamental counting principle is a rule that is used to count the total number of possible outcomes in any given situation. And what it's trying to say is that if you're originally offered an amount of options and you have m amount of options after the theorem states that you can just take end times M or multiply your amount of options together to get the total the total combinations of your options. So for this problem here we are told that there are five options for the main dish so we can allow N two equal to five And we are told that there are four choices for the beverages. So we're going to allow M- two equal to four. What the fundamental counting principle tells us is that we can just multiply our options and an M. Together and that's going to give us the total amount of combinations that these dishes can be ordered. So what we're just going to do is do five times four and five times four is going to give us 20. So that means that there are 20 possible options for ordering the meal. And that means that the answer to this problem is going to be C. So I hope this video helps you in understanding how to use the fundamental counting principle and I'll go ahead and see you all in the next video.

Use the Fundamental Counting Principle to solve Exercises 29–40. The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?

Key Concepts

Fundamental Counting Principle

Combinations of Choices

Multiplication of Options

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