The local Family Restaurant has a daily breakfast special in which the customer may choose one item from each of the following groups: Breakfast Sandwich.

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Permutations and Combinations

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Presentation transcript:

The local Family Restaurant has a daily breakfast special in which the customer may choose one item from each of the following groups: Breakfast Sandwich Sides Juice egg and ham egg and bacon egg and cheese breakfast potatoes apple slices fresh fruit cup pastry orange cranberry tomato apple grape a.) How many different breakfast specials are possible? b.) How many different breakfast specials without meat are possible?

Probability Combination

You don’t need to write down this part of the example. What is a “combination” problem? You don’t need to write down this part of the example. Suppose that I wanted to randomly choose 3 students from a class of 27. How many different groups of 3 are possible? The answer is not 27 x 26 x 25 since the order the 3 students are chosen does NOT matter. For example if we consider 3 students (A,B,C) all 6 of the following arrangements are equivalent: ABC, ACB, BAC, BCA, CAB, CBA.

Suppose that I wanted to randomly choose 3 students from a class of 27 Suppose that I wanted to randomly choose 3 students from a class of 27. How many different groups of 3 are possible? This group of 3 students got counted 6 times instead of 1. So, we must divide by 6 to get the correct answer: = 2925

Combination: Order Doesn’t Matter To find the number of combinations when choosing r objects from a total of n objects and order doesn’t matter: Number of Combinations =

Combination: Order Doesn’t Matter For example, the number of ways to choose 3 students from class of 27 is: = = 2925

Combination Problems: With Formula =

Combination Problems: With Formula

Combination Practice Problems: Keep your paper  2) In how many ways can a group of five players on the varsity boys basketball team be chosen from a team of 14 players? 3) How many ways can a group of three students be selected from a class of 21 students?

Permutation or Combination? Determine whether the following situations would require calculating a permutation or a combination: a.) Selecting three people to attend a conference in Washington, D.C. b.) Selecting a lead and an understudy for a school play. c.) Assigning students to their seats on the first day of school.

Solve each problem: Does the order matter? 1) A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters? In how many ways can 3 different vases be arranged on a tray? How many different arrangements can be made with the letters in the word EXAM?

CHALLENGE: EXTRA CREDIT There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference. a.) How many different ways are there to select a group of four students to attend the conference? b.) If the members of the club decide to send two juniors and two seniors, how many different groupings are possible?