Permutations and Combinations.  Permutation- An arrangement of objects in which order is important.  Linear Permutation- The arrangement of objects.

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Presentation transcript:

Permutations and Combinations

 Permutation- An arrangement of objects in which order is important.  Linear Permutation- The arrangement of objects or people in a line.  Combination- An arrangement of objects in which order is not important.

 Factorial is found by finding the product of all of the numbers between 1 and n.  5!  7!  3!  15!

 There are 10 finalists in a figure skating competition. How many ways can gold, silver, and bronze be awarded?

 A newspaper has nine reporters available to cover four different stories. How many ways can the reporters be assigned to cover the stories?

 The winner and first, second, and third runners-up out of 12 finalists.

 How many different ways can the letters of the word MISSISSIPPI be arranged?

 How many different ways can the letters of the word DECIDED be arranged?

 How many different arrangements of the letters of the hawaiian word ALOHA are possible?

 A group of seven students working on a project needs to choose two students to present the groups report. How many ways can they choose the two students?

 A family of septuplets assigns different chores to the children each week. How many ways can three children be chosen to help with the laundry?

 How many ways to choose 2 CDs to buy from ten that are on sale?

 In more complicated situations, you may need to multiply combinations and/or permutations.

 Five cards are drawn from a standard deck of cards. How many hands consist of 3 clubs and 2 diamonds?

 How many 5-card hands consist of 5 cards of the same suit?

 In a multi-state lottery, the player must guess which five of the forty-nine white balls numbered 1-49 will be drawn. The order in which the balls are drawn does not matter. The player must also guess which one of the forty-two red balls numbered 1-42 will be drawn. How many ways can the player fill out a lottery ticket?

 Pages  2-36 even