The Fundamental Counting Principle
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This document explains the fundamental counting principle and permutations. It provides examples of how to use the principle to calculate the number of possible outcomes for events with multiple steps or choices. These include examples like counting meal combinations, sandwich varieties, possible license plates, phone numbers, test answers, and card selections. It discusses accounting for situations where items can or cannot be repeated between choices.
The Fundamental Counting Principle
- 2. 53b Fundamental counting principle53b Fundamental counting principle You are at your school cafeteria that allows you to choose aYou are at your school cafeteria that allows you to choose a lunch meal from a set menu. You havelunch meal from a set menu. You have twotwo choices for thechoices for the Main course (a hamburger or a pizza),Main course (a hamburger or a pizza), TwoTwo choices of a drinkchoices of a drink (orange juice, apple juice) and(orange juice, apple juice) and ThreeThree choices of dessert (pie,choices of dessert (pie, ice cream, jello).ice cream, jello). How many different meal combos can you select?_________How many different meal combos can you select?_________ Method one: Tree diagramMethod one: Tree diagram LunchLunch HamburgerHamburger PizzaPizza AppleApple OrangeOrange Apple Orange PiePie IcecreamIcecream JelloJello PiePie IcecreamIcecream JelloJello PiePie IcecreamIcecream JelloJello PiePie IcecreamIcecream JelloJello 12 meals12 meals
- 3. THE FUNDAMENTAL COUNTING PRINCIPLE If you have 2 events: 1 event can occur m ways and another event can occur n ways, then the number of ways that both can occur is m*n Event 1 = 4 types of meats Event 2 = 3 types of bread How many diff types of sandwiches can you make? 4*3 = 12
- 4. 3 OR MORE EVENTS: 3 events can occur m, n, & p ways, then the number of ways all three can occur is m*n*p 4 meats 3 cheeses 3 breads How many different sandwiches can you make? 4*3*3 = 36 sandwiches
- 5. At a restaurant at Cedar Point, you have the choice of 8 different entrees, 2 different salads, 12 different drinks, & 6 different deserts. How many different dinners (one choice of each) can you choose? 8*2*12*6= 1152 different dinners
- 6. FUNDAMENTAL COUNTING PRINCIPLE WITH REPETITION Ohio Licenses plates have 3 #’s followed by 3 letters. 1. How many different licenses plates are possible if digits and letters can be repeated? There are 10 choices for digits and 26 choices for letters. 10*10*10*26*26*26= 17,576,000 different plates
- 7. HOW MANY PLATES ARE POSSIBLE IF DIGITS AND NUMBERS CANNOT BE REPEATED? There are still 10 choices for the 1st digit but only 9 choices for the 2nd , and 8 for the 3rd . For the letters, there are 26 for the first, but only 25 for the 2nd and 24 for the 3rd . 10*9*8*26*25*24= 11,232,000 plates
- 8. PHONE NUMBERS How many different 7 digit phone numbers are possible if the 1st digit cannot be a 0 or 1? 8*10*10*10*10*10*10= 8,000,000 different numbers
- 9. TESTING A multiple choice test has 10 questions with 4 answers each. How many ways can you complete the test? 4*4*4*4*4*4*4*4*4*4 = 410 = 1,048,576
- 10. ADDING MULTIPLE POSSIBILITIES How many license plates of 3 symbols (letters and digits) can be made using at least one letter in each?
- 11. PRACTICE How many ways are there to select 3 cards, one after the other, from a deck of 52 cards if the cards are not returned to the deck after being selected?