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Counting and Factorial

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Factorial Written n!, the product of all positive integers less than and equal to n. Ex: Evaluate.

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Exploration Evaluate the following without a calculator: 4! = 3! = 2! = 1! = Describe a pattern and find the answer for: 0! = 24 6 2 1 1 ÷ 4 ÷ 3 ÷ 2 ÷ 1

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Zero Factorial The zero factorial is one 0! = 1

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Counting with Factorials Ex: 6 different pictures are to be hung side-by- side along one wall. How many different arrangements are possible. The total number of ways (without repeats) to choose AND arrange n objects from a set of n objects (order matters) is:

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6-7 Permutations & Combinations M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle.

6-7 Permutations & Combinations M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle.

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