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Understanding the Counting Principal in Mathematics

Learn about the Counting Principal and how it applies to both independent and dependent events in mathematics. Explore examples like restaurant choices and vacation planning to grasp this fundamental concept.

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Understanding the Counting Principal in Mathematics

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  1. 0.4 – The Counting Principal

  2. The Fundamental Counting Principal If one event can occur m ways followed by another event that can occur n ways then the first event followed by the second can occur m·n ways.

  3. Independent Events Ex. 1 Two friends want to go out to eat and see a movie. They’ve narrowed it down between 3 different restaurants and 4 different movies. How many different possibilities are there for them?

  4. Independent Events Ex. 1 Two friends want to go out to eat and see a movie. They’ve narrowed it down between 3 different restaurants and 4 different movies. How many different possibilities are there for them? 3 · 4 = 12

  5. Ex. 2 ATM’s require a 4 digit code for usage. How many different codes are possible?

  6. Ex. 2 ATM’s require a 4 digit code for usage. How many different codes are possible? Each digit can be any digit between 0 – 9.

  7. Ex. 2 ATM’s require a 4 digit code for usage. How many different codes are possible? Each digit can be any digit between 0 – 9. 10 · 10 · 10 · 10 = 10,000

  8. Dependent Events Ex. 3A travel agency is planning a vacation package in which travelers will visit 5 cities around Europe. How many ways can the agency arrange the 5 cities along the tour?

  9. Dependent Events Ex. 3A travel agency is planning a vacation package in which travelers will visit 5 cities around Europe. How many ways can the agency arrange the 5 cities along the tour? 5 ∙ (5-1) ∙ (5-2) ∙ (5-3) ∙ (5-4)

  10. Dependent Events Ex. 3A travel agency is planning a vacation package in which travelers will visit 5 cities around Europe. How many ways can the agency arrange the 5 cities along the tour? 5 ∙ (5-1) ∙ (5-2) ∙ (5-3) ∙ (5-4) 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1

  11. Dependent Events Ex. 3A travel agency is planning a vacation package in which travelers will visit 5 cities around Europe. How many ways can the agency arrange the 5 cities along the tour? 5 ∙ (5-1) ∙ (5-2) ∙ (5-3) ∙ (5-4) 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 120

  12. Dependent Events Ex. 3A travel agency is planning a vacation package in which travelers will visit 5 cities around Europe. How many ways can the agency arrange the 5 cities along the tour? 5 ∙ (5-1) ∙ (5-2) ∙ (5-3) ∙ (5-4) 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 120 *This is called factorial, represented by “!”.

  13. Dependent Events Ex. 3A travel agency is planning a vacation package in which travelers will visit 5 cities around Europe. How many ways can the agency arrange the 5 cities along the tour? 5 ∙ (5-1) ∙ (5-2) ∙ (5-3) ∙ (5-4) 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 120 *This is called factorial, represented by “!”. 5! = 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 120

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