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)

Answers4 1

.52 1326 1

.52 22 1

.52 2613 1

.52 412 3

.52 1328 7

.52 1316 4

.52 13

a

b

c

d

e

f

g

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.

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.

Permutations Using A Diagram

• Is the line up (Ryan, Emily, Justin) different from the line up (Ryan, Justin, Emily)? Explain.

Factorials

The ! in math means to start at that number and multiply all the way down to 1.

Ex: 5!

5 4 3 2 1

120

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

5!5.

3!8!

6.4!

Using Permutation Notation• A class of 15 students must choose a president

and a vice president.

!

( )!n r

nP

n r

• The expression nPr represents the number of

permutations of n objects chosen r at a time.

• Example: 15P2

• 15 objects choosing 2 at a time

!

( )!n r

nP

n r

15 2

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

13 12 11 10 9 8 7 6 5 4 3 2 1P

15 2 15 14

210

P

Using Permutation Notation

• Simplify each expression.

12 2

10 4

9 3

1.

2.

3.

P

P

P

1. 132

2. 5040

3. 504

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

120

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.