0.4 – The Counting Principal. The Fundamental Counting Principal If one event can occur m ways followed by another event that can occur n ways then the.

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Presentation transcript:

0.4 – The Counting Principal

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.

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?

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

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.

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 – · 10 · 10 · 10 = 10,000

Dependent Events Ex. 3 A 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?

Dependent Events Ex. 3 A 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)

Dependent Events Ex. 3 A 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

Dependent Events Ex. 3 A 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

Dependent Events Ex. 3 A 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 “!”.

Dependent Events Ex. 3 A 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