Permutations 10.5 Notes

Entry Task You have 100 songs on your iPhone. How many different playlists can be created if you are choosing 5 songs? (A song played first is different than if the song is played second)

100*99*98*97*96

Example 1 You are going on vacation and you pack 3 sweaters, 4 pants, and 2 pairs of shoes. How many outfits are there?

Answer 3x4x2= 24 outfits

Example 2 Suppose a set of license plates has any three letters from the alphabet, followed by any three digits. How many different license plates are possible? 26x26x26x10x10x10 = 17,576,000 possible plates How many license plates will have no repeats of numbers or letters? 26x25x24x10x9x8=11,232,000 possible plates

Example 3 There are 5 starters on a basketball team; _______, _______, _______, _______, and _______ The announcer doesn’t want to play favorites, so he will announce their names in random order. How many possible combinations are there? 5x4x3x2x1 = 120 possible combinations OR 5! = 120

Factorial n! = n(n-1)(n-2)(n-3)…1 Example: 3! = 3*2*1=6 Note: 0! = 1

Practice – No Calculator 3! 5!/3!

Example A – Part 1 Seven flute players are performing in an ensemble. How many different ways can they be arranged? What is the probability of the names of the flute players being selected in alphabetical order? (Remember: Probability is found by dividing the number of ways an event can occur by the number of possible outcomes)

Permutations What is a permutation? An arrangement of some or all objects of a set without replacement where order matters. n is the total # objects r is # chosen

Find Permutations on your Calculator!

Example A – Part 1 (Using Permutations) Seven flute players are performing in an ensemble. How many different ways can they be arranged? What is the probability of the names of the flute players being selected in alphabetical order? (Remember: Probability is found by dividing the number of ways an event can occur by the number of possible outcomes)

Example A – Part 2 After the performance, the players are backstage. There is a bench with 4 seats. How many possible seating arrangements are there? Route 1: Counting Principle Route 2: Use Permutations!

Example A – Part 2 After the performance, the players are backstage. There is a bench with 4 seats. How many possible seating arrangements are there? Route 1: Counting Principle Route 2: Use Permutations!

Example A – Part 3 What about if the bench has 5 seats? Route 1: Counting Principle Route 2: Use Permutations!

Example A – Part 3 What about if the bench has 5 seats? Route 1: Counting Principle Route 2: Use Permutations!

Permutation Practice (No Calc)

Assignment Pg. 590 #1, 2aefg, 3ab, 4, 5, 8, 9abc, 11 Quiz 6/1 10.5-10.6 (permutations and combinations + Counting Principle)

Example B Two cards are drawn at random from a standard 52 card deck. How many possible combinations are there?

Example B – Part 2 What is the probability of drawing a 7 and a king?