1. Permutations and Combinations
Course 3
10-9
Permutations and Combinations
Warm Up #3 Thursday, 2/4/2016
Find the number of possible outcomes.
1. bagels: plain, egg, wheat, onion
meat: turkey, ham, roast beef, tuna
2. eggs: scrambled, over easy, hard boiled
meat: sausage patty, sausage link, bacon, ham
3. How many different 4–digit phone extensions are possible? 16 12
10,000

2. Homework
Factorial worksheet

3. Factorial

4. The factorial (!) of a number is the product of all the whole numbers from the number down to 1.
** 0! = 1
5! = 5 • 4 • 3 • 2 • 1
Read 5! as “five factorial.”
Reading Math

5. Additional Example 1: Evaluating Expressions Containing Factorials
Evaluate each expression.
A. 9!
9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 = 362,880 8! B. 6!
Write out each factorial and simplify.
8 •7 • 6 • 5 • 4 • 3 • 2 • 1
6 • 5 • 4 • 3 • 2 • 1
Multiply remaining factors.
8 • 7 = 56
Course 3

6. Additional Example 1: Evaluating Expressions Containing Factorials
Course 3
Permutations and Combinations
Additional Example 1: Evaluating Expressions Containing Factorials
10!
(9 – 2)! C.
10! 7!
Subtract within parentheses.
10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1
7  6  5  4  3  2  1
10 • 9 • 8 = 720

7. Subtract within parentheses.
Check It Out: Example 1 9!
(8 – 2)! C. 9! 6!
Subtract within parentheses.
9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1
6  5  4  3  2  1
9 • 8 • 7 = 504
Course 3