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Acc Math 1 EQ: What is the difference between a permutation and combination?

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Combination n is the total and r is the amount chosen A selection of objects where order is NOT important.

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On the Calculator n must be typed in first Then, Math PRB CHOICE 3 Type in r Enter

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Combinations A selection of objects in which order is not important. Example: Eight people pair up to do an assignment. How many different pairs are there?

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Example 1 How many different ways are there to select two class representatives from a class of 20 students?

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Example 2 From your class of 24, the teacher is randomly selecting 3 to help Mr. Shaw with a project. How many combinations are possible?

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Example 3 For your school pictures, you can choose four backgrounds from a list of ten. How many combinations of backgrounds are possible?

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Example 4 Coach Hill randomly selects 3 people out of his class of 20 to go to the courts and help him get ready for a tennis match. How many possibilities of people does he have?

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Example 5 probabilityThere are 28 students in your math class. Your teacher chooses 5 students at random to complete a group project. Find the probability that you and your best friend are chosen to work in the group.

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Solution The number of possible outcomes The number of favorable outcomes with both of you in it. Probability = 2,600/98,280 = 5/189

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Permutation n is the total and r is the amount chosen An arrangement or listing of objects where order IS important.

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Permutations ORDER MATTERS! Placement Examples: assigned seats, winning a race or running a race, 1 st place, 2 nd place, etc Positions Examples: President, Vice President, Secretary, Treasure Specific job/chore Examples: Hand out markers, pass out papers, etc

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Permutations Simplify each expression. a. 12 P 2 b. 10 P 4 c. At a school science fair, ribbons are given for first, second, third, and fourth place, There are 20 exhibits in the fair. How many different arrangements of four winning exhibits are possible? 12 11 = 132 10 9 8 7 = 5,040 = 20 P 4 = 20 19 18 17 = 116,280

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Permutations Example 6 There are 50 runners in a race. How many different ways can the runners finish in 1 st, 2 nd, or 3 rd ?

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Example 7 Mike is picking 4 of his 12 friends to go to the Braves game with him. How many ways can he pick the 4 friends that go with him?

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Example 8 A president and vice president are being chosen from a group of 20 people. How many ways can this be done?

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Example 9 Mr. Shaw needs 3 people from my class of 26 to come help clean up the gym. How many ways can I pick the 3 kids?

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Example 10 How many ways can you arrange 4 of the letters in the word PANTHER?

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Example 11 How many ways can you arrange all of the letters in the word FLOWER?

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Counting Principles The Fundamental Counting Principle: If one event can occur m ways and another can occur n ways, then the number of ways the events.

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