12.3 Factorial & Fundamental Counting Principles.

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12.3 Factorial & Fundamental Counting Principles

Example 1) You have 8 pants & 4 shirts. How many ways can you select a pants-AND-shirt combination? How many choices? What did you do to get that? 32 multiply 8∙4 = 32

*New problem: add the numbers to notes! 25 pants 12 shorts What about a day when you don’t care about wearing pants OR shorts? How many ways? 37 When doing this AND that – you MULTIPLY When doing this OR that – you ADD

Example 2 There are 25 dogs and 10 cats. How many ways to choose: - a dog or a cat? - a dog and then a cat? ADD = 35 MULT = 250

Example 3 There are 10 novels and 3 mysteries. How many ways to choose: - a novel and then a mystery? - a novel or a mystery? - a mystery and then another mystery? ADD = 13 MULT = 30 you pick 1, how many left to choose from? MULT = 3∙2 = 6

Example 4 Using the letters in SEQUOIA. How many ways to choose: a vowel and a consonant? a vowel or a consonant? 4-letter “words” using no letter more than once in a “word”? 5∙2 = 10 Vowels = 5 Consonants = 2 Total = = 7 Have 7 choices for 1 st letter 7, 6 choices for 2 nd letter, … 654∙∙∙= 840

Ex 5) I have 5 positions and 5 people to fill the positions Make 5 blanks: 54 ∙ = 5! 321 ∙∙∙ = 120 How many way can we select?

I have 2 positions and 5 people apply. How may ways to select? For 2 nd slot? 5How many choices for 1 st slot? 4 54 ∙= 20

Ex 6) 8 cars parallel parked along one side of street. How many ways can all 8 be arranged? 2 diff ways to solve: 1)8! 6 87 ∙ = 40,320 2) 5 4 ∙ 3 ∙ 21 ∙ ∙∙∙ What about 8 cars only 3 spots??? = = 336

TOO (Add to Notes) Using only the letters in SPAIN : In how many ways could you pick a vowel AND a consonant? In how many ways could you pick a vowel OR a consonant? How many different three-letter “words” could you form using no letter more than once in any given word? 2∙3 = = ∙ ∙ = 60

Homework Pg Q1-10, #1-14, 17 ALL #17—Make sure you read the example problem first to get the “formula” for an overlap