1 / 12

15.1 Factorial & Fundamental Counting Principles

15.1 Factorial & Fundamental Counting Principles. Factorial. ! factorial notation. 5! 3! 7! 0!. = 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1. = 120. = 3 ∙ 2 ∙ 1. = 6. = 7 ∙ 6 ∙ 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1. = 5040. = 1. Example 1. Faster: count down until reach # in denom.

yetta-turner
Download Presentation

15.1 Factorial & Fundamental Counting Principles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 15.1 Factorial & Fundamental Counting Principles

  2. Factorial ! factorial notation 5! 3! 7! 0! = 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 120 = 3 ∙ 2 ∙ 1 = 6 = 7 ∙ 6 ∙ 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 5040 = 1

  3. Example 1 Faster: count down until reach # in denom You MUST know how to do this without a calculator!

  4. Example 2 3 2

  5. Example 3 1! = 1 6 7! = 7 5 4 3 2 1 ∙ ∙ ∙ ∙ ∙ ∙ n n–1 n–6 n–3 n–4 n–5 n–2

  6. Example 4 8 6 9 7 5 4 3 2 1 n n–1 n–6 n–3 n–4 n–5 n–2 n+1 n+2

  7. Fundamental Counting Principles 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

  8. Fundamental Counting Principles What about a day when you don’t care about wearing pants OR shorts? 25 pants 12 shorts How many ways? 37 When doing this AND that – you MULTIPLY When doing this OR that – you ADD

  9. Example 5 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

  10. Example 6 There are 11 novels and 5 mysteries. How many ways to choose: - a novel and then a mystery? - a novel or a mystery? - a mystery and then another mystery? MULT = 55 ADD = 16 you pick 1, how many left to choose from? MULT = 5∙4 = 20

  11. Example 7 Vowels = 5 Consonants = 2 Total = 7 • 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 5 + 2 = 7 7 ∙ 6 ∙ 5 ∙ 4 = 840 Have 7 choices for 1st letter , 6 choices for 2nd letter, …

  12. Homework 11-8 Worksheet & Exercise 15-1 WS

More Related