Fri 4/29 Lesson 11 – 1 Learning Objective: To use permutations & combinations to count possibilities Hw: 11-1 Fundamental Counting WS.

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Fri 4/29 Lesson 11 – 1 Learning Objective: To use permutations & combinations to count possibilities Hw: 11-1 Fundamental Counting WS

Algebra II

 To use combination & permutation to count possibilities

# of Letters in Alphabet26 # of Digits10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

When doing this AND that – you MULTIPLY When doing this OR that – you ADD

1. There are 25 dogs and 10 cats DogCat a. How many ways to choose a dog or a cat? = 35 ways DogCat b. How many ways to choose a dog and then a cat? = 250 ways

2. There are 11 dramas & 5 comedies Drama Comedy 11 5 a. How many ways to choose a drama and then a comedy? = 55 ways Drama Comedy 11 5 b. How many ways to choose a comedy or a drama? = 16 ways Drama c. How many ways to choose a drama and then another drama? = 110 ways

3. You have 3 shirts & 2 pairs of jeans. How many possible outfits? ShirtJeans 3 2 = 6 possible outfits S1 J1 S2 J1 S3 J1 S1 J2 S2 J2 S3 J2 4. License plate has two letters followed by four digits. How many possible plates? Letter 26 = 6,760,000 Different Plates Digit 10

4. License plate has two letters followed by four digits. How many possible plates if not letters or numbers are repeated? Letter = 3,276,000 Different Plates Digit

Permutation – arrangement of items in a particular order (Order matters) n!  n factorial = 120 0! = 1 Arrange r items out of n total items

4. How many different ways to order 8 books on a shelf? 8 7 = 40, Or 8! = 40, P 2 = 20

6. 10 students racing, how many ways can the first three places finish? = P people running for VP & P = P 2

Combination – selection in which order does not matter Choosing r items out of n total items

8. 8 C 3 = 56 ( ) = 3003 ( )

10. How many ways to choose 5 people out of 30 to put into a group? 30 C 5 = 142, How many different nine player batting orders can be chosen from a baseball team of 16? 16 P 9 = 4,151,347,200

12. You have 10 pairs of shoes, 7 pairs of jeans, and 5 shirts. How many possible outfits? 10 P 1 5P15P1 7P17P1 = flavors of ice cream. How many ways to mix 3 flavors. 31 C 3 = 4495