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Fundamental Counting Principle

Fundamental Counting Principle. Example 1 A:. License plates are being produced that have a single letter followed by three digits. All license plates are equally likely. Find the number of possible license plates. Use the Fundamental Counting Principal. second digit. letter. first digit.

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Fundamental Counting Principle

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  1. Fundamental Counting Principle

  2. Example 1 A: License plates are being produced that have a single letter followed by three digits. All license plates are equally likely. Find the number of possible license plates. Use the Fundamental Counting Principal. second digit letter first digit third digit 26 choices 10 choices 10 choices 10 choices 26 • 10 •10 • 10 = 26,000 The number of possible 1-letter, 3-digit license plates is 26,000.

  3. 1 • 10 •10 • 10 26,000 P(Q ) = =  1 26 Example 1 B: Find the probability that a license plate has the letter Q. 0.038

  4. There are 9 choices for any digit except 3. 18,954 P(no 3) = = 0.729 26,000 Example 1 C: Find the probability that a license plate does not contain a 3. First use the Fundamental Counting Principle to find the number of license plates that do not contain a 3. 26 •9•9•9 = 18,954 possible license plates without a 3

  5. The Fundamental Counting Principle tells you only the numberof outcomes in some experiments, not what the outcomes are. A treediagram is a way to show all of the possible outcomes.

  6. Example 2: You have a photo that you want to mat and frame. You can choose from a blue, purple, red, or green mat and a metal or wood frame. Describe all of the ways you could frame this photo with one mat and one frame. You can find all of the possible outcomes by making a tree diagram. There should be 4 •2 = 8 different ways to frame the photo.

  7. Example 2: Each “branch” of the tree diagram represents a different way to frame the photo. The ways shown in the branches could be written as (blue, metal), (blue, wood), (purple, metal), (purple, wood), (red, metal), (red, wood), (green, metal), and (green, wood).

  8. On your own… Flip your paper over and do this on the back: A baker can make yellow or white cakes with a choice of chocolate, strawberry, or vanilla icing. Describe all of the possible combinations of cakes. You can find all of the possible outcomes by making a tree diagram. There should be 2 •3 = 6 different cakes available.

  9. Does your paper look something like this? yellow cake The different cake possibilities are (yellow, chocolate), (yellow, strawberry), (yellow, vanilla), (white, chocolate), (white, strawberry), and (white, vanilla). vanilla icing chocolate icing strawberry icing white cake vanilla icing chocolate icing strawberry icing

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