1. Warm-Up #5
4P3 8P3 =
In how many ways can 3 males (Joe, Jerry John) and 3 females (Jamie, Jenny, Jasmine) be seated in a row if the genders alternate down the row?
Five different stuffed animals are to be placed on a circular display rack in a department store. In how many ways can this be done?
0.07 72 24

2. Find the number of unique permutations of the letters in BILLIONAIRE
A baby presses 6 of the ten numbers (zero through nine). How many different number sequences could she have dialed?
4P3 8P5 =
Warm-Up #6 Tuesday, 2/16
3,326,400
1,000,000

3. Homework Tuesday, 2/16/2016
Advanced: Lottery Permutations vs Combinations Regular: Combinations packet page 1 and 2

4. Combinations

5. RECAP ON PERMUTATIONS
The order in which the items is being arranged does matter
Linear permutations: nPr = 𝒏! 𝒏−𝒓 !
Identical permutations: 𝒏! 𝒓 𝟏 ! 𝒓 𝟐 ! 𝒓 𝟑 !
Circular permutations: (n-1)!

6. Example
You have 3 letters. A B C. Write all of the combinations. A B C A C B B A C B C A C A B C B A
How many different combinations can I make if the order of the letters does matter?
Permutations: 6 ways
How many different combinations can I make if the order of the letters does not matter?
Combination: 1 way

7. A combination is a selection of things in any order
A combination is a selection of things in any order. The order does not matter. You only care about how “groups” you can make.

8. Permutations and Combinations
Course 3
10-9
Permutations and Combinations

9. Additional Example 3A: Finding Combinations
Permutations and Combinations
Additional Example 3A: Finding Combinations
Mary wants to join a book club that offers a choice of 10 new books each month.
If Mary wants to buy 2 books, find the number of different pairs she can buy.
10 possible books
10!
2!(10 – 2)! =
10!
2!8!
10C2 =
2 books chosen at a time
10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1
(2 • 1)(8 • 7 • 6 • 5 • 4 • 3 • 2 • 1) =
= 45
There are 45 combinations. This means that Mary can buy 45 different pairs of books.

10. Additional Example 3B: Finding Combinations
If Mary wants to buy 7 books, find the number of different sets of 7 books she can buy.
10 possible books
10!
7!(10 – 7)! =
10!
7!3!
10C7 =
7 books chosen at a time
10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1
(7 • 6 • 5 • 4 • 3 • 2 • 1)(3 • 2 • 1) =
= 120
There are 120 combinations. This means that Mary can buy 120 different sets of 7 books.

11. Check It Out: Example 3A
Harry wants to join a DVD club that offers a choice of 12 new DVDs each month.
If Harry wants to buy 4 DVDs, find the number of different sets he can buy.
12 possible DVDs
12!
4!(12 – 4)! =
12!
4!8!
12C4 =
4 DVDs chosen at a time =
12 • 11 • 10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1
(4 • 3 • 2 • 1)(8 • 7 • 6 • 5 • 4 • 3 • 2 • 1)
= 495

12. Check It Out: Example 3A Continued
Course 3
Permutations and Combinations
Check It Out: Example 3A Continued
There are 495 combinations. This means that Harry can buy 495 different sets of 4 DVDs.

13. Permutations and Combinations
Course 3
Permutations and Combinations
Check It Out: Example 3B
If Harry wants to buy 11 DVDs, find the number of different sets of 11 DVDs he can buy.
12 possible DVDs
12!
11!(12 – 11)! =
12!
11!1!
12C11 =
11 DVDs chosen at a time =
12 • 11 • 10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1
(11 • 10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1)(1)
= 12

14. Check It Out: Example 3B Continued
Course 3
Permutations and Combinations
Check It Out: Example 3B Continued
There are 12 combinations. This means that Harry can buy 12 different sets of 11 DVDs.

15. Example
How many different ways are there to purchase 2 CDs, 3 cassettes, and 1 videotape if there are 7 CD titles, 5 cassette titles, and 3 videotape titles? Answer: (7C2)(5C3)(3C1)= 630 ways