1. Counting and Factorial

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

3. 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

4. Zero Factorial The zero factorial is one 0! = 1

5. 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: