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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? = = 5,040 = 20 P 4 = = 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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