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Bellwork

Bellwork. Remember that class begins when you enter the classroom. 1) At a sporting goods store, skateboards are available in 8 different deck designs. Each deck design is available with 4 different wheel assemblies. How many skateboard choices does the store offer?

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Bellwork

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  1. Bellwork Remember that class begins when you enter the classroom. 1) At a sporting goods store, skateboards are available in 8 different deck designs. Each deck design is available with 4 different wheel assemblies. How many skateboard choices does the store offer? 2) You would like to go to a movie, a play, or the zoo. You can go with your cousin, your brother, or your friend. You can go on Friday, Saturday, or Sunday. How many different options do you have?

  2. Solutions: • Multiply the number of deck designs (8) and the number of wheel assemblies (4). So the store offers 32 skateboard choices. • Multiply the number of places you can go to, times the number of different people you can go with, times the number of different days you can you on: 3 * 3 * 3 = 27 different options.

  3. There are two Counting Principles: • The multiplication counting principle • The addition counting principle

  4. We’ve already been using the multiplication counting principle. Today’s bellwork was an example. Let’s look at the definition: Multiplication counting principle: If one event can occur in m ways and another even can occur in n ways, then the number of ways that both events can occur together is m x n.

  5. Multiplication counting principle: If one event can occur in m ways and another even can occur in n ways, then the number of ways that both events can occur together is m * n. For example: On your history test you can choose one of 4 essay questions and one of 5 extra credit questions. How many choices do you have: The first event is choosing your essay question, and there are 4 choices, so m=4. The second even is choosing your extra credit question, and there are 5 choices, so n=5. The total number of choices you have is m*n = 4*5 = 20.

  6. At a shoe store, shoes are available in 6 different styles and 3 different colors. How many choices does the shoe store offer?

  7. Before we define the addition counting principle, let’s look at a few examples: Every student at Osborne is given an id code consisting of 3 symbols (first a letter and then two digits). How many different id codes are possible?

  8. Every student at Osborne is given an id code consisting of 3 symbols (letters and digits). How many different id codes are possible if at least one letter is used in each? The code looks like this: LDD How many letters are there to choose from? 26 How many numbers do we have to choose from for each digit? 10 So we have 26 x 10 x 10 different codes. 26 x 10 x 10 = 2600

  9. What if we need more id codes??? Every student at Osborne is given an id code consisting of 3 symbols (letters and digits). How many different id codes are possible if at least one letter is used in each?

  10. Every student at Osborne is given an id code consisting of 3 symbols (letters and digits). How many different id codes are possible if at least one letter is used in each? To find the number of codes, first determine the number of ways each code can be made. We can have either a letter (L) or a digit (D). There are 26 different letters and 10 different digits (0-9). Each code must have at least one letter, so we have: LDD, DLD, DDL, LLD, LDL, DLL, LLL

  11. Vocabulary • Addition counting principle: If the possibilities being counted can be split into different groups, then the total number of possibilities is the sum of the numbers of possibilities for each group.

  12. Class Example Let’s pretend that I am getting to choose 4 students from this class to be given a free homework pass. I must choose at least 1 boy and 1 girl. Based on the students in this room, how many different ways can I choose this group?

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