1. Warm Up May 7 1. A card is drawn from a well-shuffled deck of 52 cards. Find the probability that the card is: a) A 7 b) Red c) A red 8 d) A spade e) A face card (K, Q, J of any suit) f) black or a 2 g) Less than a 5 (consider aces as one)

2. Answers

3. 14.4 Permutations A permutation is an arrangement of a set of objects in a particular order. –In a permutation the order of the objects/items is important. –If you order an ice cream cone, ordering chocolate first and then vanilla will give you a different ice cream cone than vanilla first and then chocolate.

4. Permutations Using A Diagram In how many ways can Ryan, Emily and Justin line up in the gym class? Ryan, Emily and Justin can line up in six different ways. This means that there are six permutations.

5. Permutations Using A Diagram Is the line up (Ryan, Emily, Justin) different from the line up (Ryan, Justin, Emily)? Explain.

6. Factorials The ! in math means to start at that number and multiply all the way down to 1. Ex: 5! 120

7. You try: Simplify each expression. 1.3! 2.6! 3.4! 4.8! 1.6 2.720 3.24 4.40320 5.20 6.1680

8. Using Permutation Notation A class of 15 students must choose a president and a vice president. The expression n P r represents the number of permutations of n objects chosen r at a time. Example: 15 P 2 15 objects choosing 2 at a time

10. Using Permutation Notation Simplify each expression. 1. 132 2. 5040 3. 504

11. Try these: 1.Aaron has 6 autographed baseballs and room for 4 on a shelf. How many arrangements can he make? 2.How many ways can 5 people line up for a picture? 3.They are 6 people running for President, Vice President, and Secretary. How many ways can they be picked? 360 120

12. Summary: Answer in complete sentences. What is a permutation? Write the notation you could use to show the permutation of t things taken c at a time.