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 007 72 24 WarmUp 6 Tuesday 216 Find the number of uni ID: 723410
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Warm-Up #5
= 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
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Warm-Up #6 Tuesday, 2/16
Find the number of unique permutations of the letters in BILLIONAIREA baby presses 6 of the ten numbers (zero through nine). How many different number sequences could she have dialed?
=
3,326,400
1,000,000
Slide3
Homework Tuesday, 2/16/2016
Advanced: Lottery Permutations vs CombinationsRegular: Combinations packet page 1 and 2Slide4
Combinations Slide5
RECAP ON PERMUTATIONS
The order in which the items is being arranged does matterLinear permutations: nPr =
Identical permutations:
Circular permutations: (n-1)!
Slide6
Example
You have 3 letters. A B C. Write all of the combinations.A B CA C BB A CB C AC A BC B AHow 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 waySlide7
A
combination is a selection of things in any order. The order does not matter. You only care about how “groups” you can make. Slide8
Course 3
10-9
Permutations and CombinationsSlide9
Additional Example 3A: Finding Combinations
Permutations and 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
2 books chosen at a time
10!
2!(10 – 2)!
=
10!
2!8!
=
10
•
9
•
8
•
7
•
6
•
5
•
4
•
3
•
2
•
1
(2
•
1)(8
•
7
•
6
•
5
•
4
•
3
•
2
•
1)
10
C
2
=
= 45
There are 45 combinations. This means that Mary can buy 45 different pairs of books.Slide10
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
7 books chosen at a time
10!
7!(10 – 7)!
=
10!
7!3!
10
C
7
=
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.Slide11
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
4 DVDs chosen at a time
12!
4!(12 – 4)!
=
12!
4!8!
=
12
•
11
•
10
•
9
•
8
•
7
•
6
•
5
•
4
•
3
•
2
•
1
(4
• 3 •
2
•
1)(8
•
7
•
6
•
5
•
4
•
3
•
2
• 1)
12C4 =
= 495Slide12
Check It Out: Example 3A Continued
Course 3
Permutations and Combinations
There are 495 combinations. This means that Harry can buy 495 different sets of 4 DVDs.Slide13
Check It Out: Example 3B
Course 3
Permutations and Combinations
If Harry wants to buy 11 DVDs, find the number of different sets of 11 DVDs he can buy.
12 possible DVDs
11 DVDs chosen at a time
12!
11!(12 – 11)!
=
12!
11!1!
=
12
•
11
•
10
•
9
•
8
•
7
•
6
•
5
•
4
•
3
•
2
•
1
(11
• 10 •
9
•
8
•
7
•
6
•
5
•
4
•
3
•
2
• 1)(1)
12C11
=
= 12Slide14
Check It Out: Example 3B Continued
Course 3
Permutations and Combinations
There are 12 combinations. This means that Harry can buy 12 different sets of 11 DVDs.Slide15
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