Counting. Meat Cheese Bread

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1 Name: Date: Counting The Fundamental Counting Principle states that if one event has m possible outcomes and a second independent event has n possible outcomes, then there are m x n total possible outcomes for the two events together. Example 1: Jan wants to make a pizza. At the pizza bakery, she can choose from 4 types of meat, 2 types of cheese and 2 types of bread. How many different pizza combinations can she make if she chooses one from each category? X X = Meat Cheese Bread MMC Topic 2 Counting 1

2 Tree Diagram for Example 1 16 Combinations of Pizza MMC Topic 2 Counting 2

3 Hint 1: How many digits are there (0-9)? Hint 2: How many letters are in the alphabet (A-Z)? Hint 3: How many vowels are in the alphabet? Hint 4: How many consonants are in the alphabet? Example 2: How many license plates can you make with 1 digit followed by 1 letter? X = Digits Letters Steps for Solving Counting Problems 1. Determine how many categories. a. Shirts, Pants, Shoes = 3 categories b. License plate with 3 digits and 2 letters = 5 categories c. 4 students standing in line = 4 spots in line 2. Draw a line for each category. 3. Record the number of options for each category. 4. Multiply.! MMC Topic 2 Counting 3

4 Problem Sets 1. In how many ways can two coins come up when flipped? 2. In how many ways can three coins come up when flipped? 3. In how many ways can six coins come up when flipped? 4. In how many ways can a red die and a green die be rolled? 5. In how many ways can a die be rolled and a coin be flipped? 6. How many four-letter words are there? (You do not need to multiply it out.) words = does not have to be a word from the dictionary 7. How many four-letter words are there without repeating the same letter twice? (You do not need to multiply it out.) 8. How many four-letter words are there with vowels in the middle two spaces and a consonant at the end? (You do not need to multiply it out.) MMC Topic 2 Counting 4

5 9. How many lock combinations can you make with four digits? 10. How many lock combinations can you make with 2 digits followed by 2 letters? (You do not need to multiply it out.) 11. In how many ways can Michelangelo give five differently colored M&M s to five kids? 12. How many ways can 3 students sit on a roundtable? 13. How many ways can 4 students sit on a roundtable? 14. Malia is making hamburgers for dinner. Her family can have their hamburger with either provolone cheese, swiss cheese, jarlsburg cheese or no cheese. Lettuce, tomato, onions or none can be added as toppings. How many possible hamburger combinations are there? MMC Topic 2 Counting 5

6 15. Jacy went into Subway to order a sandwich. She had the following choices of topping for her sandwich: lettuce, pickle, tomato, onion and mushrooms. How many combinations of 2 different toppings could Jacy choose to put on her turkey sandwich? 16. Travis has a red t-shirt, a green t-shirt, a blue t-shirt and an orange t-shirt. He has green, blue and black jeans. How many different combinations of outfits can he wear? 17. In how many different ways can the five cars of a five-car train be arranged? 18. Dawson, Ethan and Peyton want to have a picture taken in the Funny Photo Booth but can t decide in what order to sit. If each picture costs $1.50, how much will their Dad pay to have pictures of them in every possible order? 19. Ethel made a list of all the whole numbers from 1 to 100. How many times did she write the digit 2? MMC Topic 2 Counting 6

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