Counting Principle/ Permutations and Combinations
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1 Counting Principle/ Permutations and Combinations T.S. Demonstrate Understanding of Concept AutoSave 1
2 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? AutoSave 2
3 2.)A ballot has four candidates for President and two for vice president. How many different combinations are possible? AutoSave 3
4 The Counting Principle If 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: AutoSave 4
5 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 side by side in the photo? 4.) How many possible outcomes are there for rolling two dice? AutoSave 5
6 Consider these... 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? AutoSave 6
7 Permutations An arrangement in which order is important. Line up 4 people... Marty Sally Frank Linda 1st in line 2nd in line 3rd in line 4th in line When using all people, or things, in the group then the Counting Principle applies. AutoSave 7
8 Permutations What happens if you are not using people, or things, in a group? Out of 4, line up 2 people... Marty Sally Frank Linda 1st in line 2nd in line AutoSave 8
9 Permutation Notation: np r n = number of members r = number choosing 1.) There are 5 people in a group, only 2 can be lined up. How many different ways can you line them up? 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 3 number arrangements are possible if no number can be repeated? AutoSave 9
10 Combinations an 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 Sally Marty Frank Marty Frank Sally Sally Frank Marty Frank Frank Marty Sally Sally Marty AutoSave 10
11 Combination Notation nc r 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? AutoSave 11
12 Practice... 1.) 6 P 2 2.) 5 P 4 3.) 7 C 3 4.) 6 C 4 5.) You have 9 books and want to display 5 on a shelf. How many different 5 book 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, vice president, secretary and treasurer. From a class of 25 students, how many different groups of officers could students elect? AutoSave 12
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