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8.4 Permutations Factorial Notation For any natural number n, * 0! = 1 1 Permutation: A set of n objects in an ordered arrangement of a certain number of objects. Formula: The number of permutations of a set of n objects taken k at a time is given by 2 Permutations on the Calculator math ⇒PRB ⇒ nPr 3 Fundamental Principle of Counting 1.) An auto manufacturer produces 7 models, each available in 6 different colors, 4 different upholstery fabrics, and 5 interior colors. How many different automobile varieties are available? 2.) A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different 3-course meals are possible? 3.) A 5-digit zip code contains 5 numbers 0-9 which can be repeated. How many different possible zip codes are there? 4.) How many different 4 letter arrangements can be written if letters can be repeated? 4 Permutations How many ways can you arrange 8 people in a straight line? Your mom gives you a list of chores that must be done: vacuum, wash dishes, take out the trash, clean your room, walk to dog, dust, and sweep the floors. She tells you that you must complete 4 of the chores. How many different ways can you arrange the chores? 5 Permutations: More Examples How many different ways can 9 baseball players be arranged on the baseball field? If there are 15 people on the team, how many ways can they be assigned to 9 positions? 6