Tree Diagrams and Fundamental Counting Principle

Fundamental Principle of counting

By Eliada Falcon

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Use a tree diagram to find the number of ways to choose a sandwich and a drink, if the sandwiches are turkey, ham, and chicken and the drinks are soda and lemonade.

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Fundamental Counting Principle: Definition & Examples - Video Lesson

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A fast-food restaurant has a meal special: $5 for a drink, a sandwich, side item and dessert.

The choices are:

Sandwich: Grilled chicken, All Beef Patty, Vegeburger and Fish Filet.

Side: Regular fries, Cheese Fries, Potato Wedges.

Dessert: Chocolate Chip Cookie or Apple Pie.

Drink: Fanta, Dr. Pepper, Coke, Diet Coke and Sprite.

Q. How many meal combos are possible?

Answer

There are 4 stages:

1. Choose a sandwich.

2. Choose a side.

3. Choose a dessert.

4. Choose a drink.

There are 4 different types of sandwich, 3 different types of side, 2 different types of desserts and five different types of drink.

The number of meal combos possible is 4 x 3 x 2 x 5 = 120.​

Determine the number of arrangements using the principle of counting.

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Q. You take a survey with five “yes” or “no” answers. How many different ways could you complete the survey?

Answer

There are 5 stages:

Question 1, question 2, question 3, question 4, and question 5.

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There are 2 choices for each question (Yes or No).

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So the total number of possible ways to answer is: 2 x 2 x 2 x 2 x 2 = 32.​

Determine the number of arrangements using the principle of counting.

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Q: A company puts a code on each different product they sell. The code is made up of 3 numbers and 2 letters. (example: 002TH) How many different codes are possible?

Answer

There are 5 stages

(number 1, number 2, number 3, letter 1 and letter 2).

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There are 10 possible numbers: 0 – 9.

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There are 26 possible letters: A – Z.

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So we have: 10 x 10 x 10 x 26 x 26 = 676, 000 possible codes.​

Determine the number of arrangements using the principle of counting.

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How many license plates are possible?

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How many phone numbers are possible?

Work on Skill Check 3, p. 431.

Solve it in your notebook. ​

You can work in pairs.