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Counting Principle 1.Suppose you have three shirts (red, black, and yellow) and two pair of pants (jeans and khakis). Make a tree diagram to find the number.

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Presentation on theme: "Counting Principle 1.Suppose you have three shirts (red, black, and yellow) and two pair of pants (jeans and khakis). Make a tree diagram to find the number."— Presentation transcript:

1 Counting Principle 1.Suppose you have three shirts (red, black, and yellow) and two pair of pants (jeans and khakis). Make a tree diagram to find the number of possible outfits you have. SHORTCUT!!! Multiplication Counting Principle If there are m ways to make a first selection and n ways to make a second selection, there are m x n ways to make the 2 selections.

2 2.Mary has 3 pair of pants, 4 shirts and 2 pair of shoes. How many combinations of outfits can she make with her current wardrobe? 3.Ron has five different types of pasta and three different types of sauces, and fixings for two different types of salads. How many different combinations of meals could he make? 4.At a neighborhood pizza shop, there are five vegetable toppings and three meat toppings for a pizza. How many different pizzas can you order with one meat and one vegetable? 5.Jim is planning on ordering a new truck. He has a choice of 4 exterior colors, 2 interior colors, and two kinds of seats. How many combinations does he have to pick from?

3 Permutation: Example and explanation: How many ways can you line up 6 students? There are 6 choices for the first position, 5 for the second, 4 for the third, 3 for the fourth, 2 for the fifth and 1 for the sixth. The answer is 6! = Six Factorial... or in other words... 6 x 5 x 4 x 3 x 2 x 1 = 720. 1.How many different batting orders can you have with 9 baseball players? 2.How many ways can you arrange four books on a bookshelf? 3.In how many ways can you select a right, center and left fielder from 8 players on a baseball team? To answer this question, you need to find the number of permutations of 8 objects (players) arranged 3 at a time. See the notation explanation below! An arrangement of objects in a specific order WHEN ORDER MATTERS!

4 5.Suppose you use six different letters to make a computer password. Find the number of possible six-letter passwords. 6.Suppose your cousin needs to choose a four-digit number to use with a new debit card. Find the number of possible four-digit numbers without repeating a digit. 7.Is a six-letter password or a six-digit number harder for someone to guess? Explain. Permutation Notation Represents the number of permutations of n objects arranged r at a time= n ( n – 1 ) ( n – 2 )... stop when you have r factors


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