Chapter 7: Probability Lesson 8-6: Combinations Mrs. Parziale.

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Presentation transcript:

Chapter 7: Probability Lesson 8-6: Combinations Mrs. Parziale

Vocabulary: Permutation – A collection of objects in which the order of the objects DOES matter. Combination – a collection of objects in which the order of the objects DOES NOT matter.

Combinations Choosing a 4 member executive branch Giving the top 3 finishers the same prize Numbers in a lottery drawing Recognizing a group of top 10% in class Permutations Choosing a Pres, VP, Sec, and Tres. Awarding 1 st, 2 nd, and 3 rd prize Locker “combination” Recognizing #1 – 20 highest GPA

Example 1: Which is the permutation, which is the combination problem? a. You have six colors to choose from and you wish to choose three for a flag. How many choices of colors are possible? b.A flag with stripes of three different colors can use any one of six colors. How many flags are possible? c. A shopkeeper is rearranging a display of 8 vases in the shop window. How many different displays can she make?

Example 1, cont. d. A swim team has 6 swimmers that can swim freestyle. The coach must pick three swimmers to swim in the next heat. How many different groups of three swimmers does he have to choose from? e. A pizza shop offers the following toppings – cheese, pepperoni, mushroom, sausage, peppers, and onions. How many different pies with two toppings can he offer? f. How many different ways can a set of 10 books be organized on a shelf?

Example 2: How many ways can 6 people shake hands with everyone exactly once?

Example 3: Twenty distinct points are chosen on a circle a)How many segments are there with these points as endpoints? b)How many triangles are there with these points as vertices? c) How many quadrilaterals are there with these points as vertices?

Example 4: You can order pizza with a choice of 9 toppings. How many different pizzas are possible with exactly 3 toppings? (Order doesn’t matter with pizza toppings)

Closure Five students from your class of 25 are randomly picked to be interviewed by the local newspaper. What is the probability that neither you nor your best friend in the class will be picked? # of ways to pick 5 people without picking you or your friend = # of ways to pick 5 people from the whole class = Probability =