1. Permutations With your group find as many arrangements of the letters A, H, M, T as you can. How many 2 letter arrangements are there? Could you do this an easier way? Use a tree diagram, or…

2. Key Terms: Permutation: is any arrangement of items or events Notation: P(n,r) or nPr – n tells you what number to start with, r tells how many numbers you are multiplying Factorial: the product of a whole number and every positive number less than itself. Notation- x! – 0! = 1

3. Examples: How many different ways can the letters of each word be arranged? 1. SAND 2. GREEN 3. CAT 4! = 4 ● 3 ● 2 ● 1 = 24 5! = 5 ● 4 ● 3 ● 2 ● 1 = 120 3! = 3 ● 2 ● 1 = 6

4. Examples: Find the value. 4. 7! 5. P(8,2) 6. P(9, 3) 7 ● 6 ● 5 ● 4 ● 3 ● 2 ● 1 = 5040 8 ● 7 = 56 9 ● 8 ● 7 = 504

5. Examples: 7. In how many ways can six people line up for a photograph? 8. A building inspector is supposed to inspect 10 building for safety code violations. In how many different orders can the inspector visit the buildings? 6! =6●5●4●3●2●16●5●4●3●2●1 720 ways 10 ! =10 ● 9 ● 8 ● 7 ● 6 ● 5 ● 4 ● 3 ● 2 ● 1 = 3,628,800 ways

6. Examples: 9. How many 3 letter words can you make from 5 letters? 10. How many 4-letter, two digit license plate numbers can you make? P(5, 3) 5●4●35●4●3 60 words 26 ● 26 ● 26 ● 26 ● 10 ● 10 a. If repeat letters and numbers allowed b. If repeat letters and numbers not allowed 26 ● 25 ● 24 ● 23 ● 10 ● 9 45,697,600 plates 32,292,000 plates