13.2 Fundamental Counting Principle
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Counting Different Choices and Combinations, Summaries of Mathematics
Various scenarios where the number of choices or combinations needs to be calculated. It covers examples of ice cream flavors and toppings, flipping coins, making outfits, and creating license plates. The document also introduces the concept of a slot diagram for keeping track of the different ways to do each task.
What you will learn
- How many different ways can you flip 4 coins?
- How many different ways can you pick a flavor and a topping at an ice cream shop?
- What is the concept of a slot diagram and how is it used to keep track of different combinations?
- How many different license plates can be made with 3 letters and 3 numbers, where each letter and number is unique?
- How many different outfits can you make with 3 coats, 5 pants, 7 shirts, and 4 ties?
Typology: Summaries
2021/2022
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13.2 Fundamental Counting Principle
At an Ice Cream shop they have 5 different flavors of ice cream and you can pick one of 4 toppings. How many choices do you have? 5 choices of flavors, 4 choices of toppings 5x4 = 20
How many ways can you flip 4 coins?
Someone wants to know how many different outfits they can make with 3 coats, 5 pants, 7 shirts, and 4 ties. How many different outfits?
Someone wants to know how many different outfits they can make with 3 coats, 5 pants, 7 shirts, and 4 ties.
Example: The combination for a keypad is 5 digits long. Suppose that you any digit (0-9) for the numbers. How many different combinations are there?
Example: The combination for a keypad is 5 digits long. Suppose that you any digit (0-9) for the numbers. There are 10x10x10x10x10 = 100000 combinations.
Example: The combination for a keypad is 5 digits long. Suppose that you any digit (0-9) for the numbers. Now the first digit cannot be 0. There are 9x10x10x10x10 = 90000 combinations.
Example: A license plate has 3 letters followed by three numbers. How many different license plates are there?
Example: A license plate has 3 letters followed by three numbers. Every letter and number must now be unique. How many different license plates are there?
Example: A license plate has 3 letters followed by three numbers. Every letter and number must now be unique. How many different license plates are there? 26 x 25 x 24 x 10 x 9 x 8 = 11,232,