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Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
Counting Principle/Permutations and
CombinationsT.S. Demonstrate Understanding of Concept
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
1.) Paul has three tops, one red, one green, and one blue. He also has four pairs of pants: one white, one black, one blue and one brown. List all the different outfits he can make. How many outfits can he make?
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
2.)A ballot has four candidates for President and two for vice president. How many different combinations are possible?
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
The Counting PrincipleIf there are m ways of making one choice, and n ways of making a second choice, then there are m n ways of making the 1st choice followed by the second.
Outfits:
President/VP:
Standing in Line:
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
1.) There are three hats, two pairs of shoes and, four dresses in the dress box. How many different outfits can Wendy make?
2.) How many different 7 digit phone numbers can you make?
3.) Four Olympic gold medalist will pose together for a picture. How many different ways can they stand sidebyside in the photo?
4.) How many possible outcomes are there for rolling two dice?
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
When lining 3 people up in line does the order matter?
How about just selecting 3 people, does order matter then?
When putting books on a shelf, does order matter?
In the Olympics, does order matter in swimming heats?
How about, in the gold medal swimming finals?
Consider these....
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
PermutationsAn arrangement in which order is important.
Line up 4 people...
1st in line 2nd in line 3rd in line 4th in line
Marty Sally Frank Linda
When using all people, or things, in the group then the Counting Principle applies.
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
PermutationsWhat happens if you are not using people, or things, in a group?
Out of 4, line up 2 people...
1st in line 2nd in line
Marty Sally Frank Linda
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
Permutation Notation:
1.) There are 5 people in a group, only 2 can be lined up. How many different ways can you line them up?
nPrn = number of members r = number choosing
2.) There are 6 contestants competing for the title of Little Miss. The 1st, 2nd and 3rd place winners get metals. How many permutations are there for the winners?
3.) There are 50 numbers on a standard combination lock. How many 3number arrangements are possible if no number can be repeated?
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
Combinationsan arrangement in which order does not matter
Out of 4 people, select 2... Marty Sally Frank Linda
Out of 4 people, select 3.....
Marty Sally Frank
Marty SallyFrank
Sally Marty Frank
Sally Frank Marty
MartySallyFrank
Marty SallyFrank
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
Combination NotationnCr
n = number of members r = number choosing
1.) In a class of 22 students, I need to select 3. How many combination of students are there?
2.) At the local pizza place, they have 9 different topping. You can order a pizza with 3 different toppings for $10. How many different types of pizza can be made?
3.) The DJ has 40 songs from the 80's. He needs to play exactly 5 songs at the dance. How many 5 song combination can he make if the order he plays the songs does not matter?
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
Practice...
1.) 6P2 2.) 5P4 3.) 7C3 4.) 6C4
5.) You have 9 books and want to display 5 on a shelf. How many different 5book arrangements are possible?
6.) You have 5 choices of sandwiches fillings. How many different sandwiches could you make by choosing three of the five fillings?
7.) Mr. Cataldi selects a committee of 4 students from 25 students. How many different committees could he make?
8.) Class officers are president, vicepresident, secretary and treasurer. From a class of 25 students, how many different groups of officers could students elect?
Day 5 Counting Principle Permutations and Combinations per 7
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April 10, 2012
