Lesson # 64 – 65 Notes Permutations and Combinations 1.The Counting Principle – The number of outcomes for an event is the product of the number of outcomes for each stage of the event. Example : Flip a coin and roll a number cube. The coin has 2 sides, the cube has 6 sides. The total number of possible outcomes is The total number of possible outcomes is 2 x 6 = 12 2 x 6 = 12

Try this one Try this one Martha is selecting the menu for a banquet. Her choices are: entrée: chicken, beef, fish salad: Caesar, house side dish: rice, vegetables, pasta dessert: cake, pie, ice cream How many different meals of one entrée, salad, side dish, and dessert could Martha order?

Answer: entrée: chicken, beef, fish = 3 choices salad: Caesar, house = 2 choices side dish: rice, vegetables, pasta = 3 choices dessert: cake, pie, ice cream = 3 choices 3 x 2 x 3 x 3 = 54 choices

Factorial Notation – 2. The expression n! is the product of all numbers starting with n and counting backward to 1. The symbol for factorial is the exclamation point. The expression “5!” is read “five factorial.” Example – 5! = 5 x 4 x 3 x 2 x 1 = 120

Try this one Kelly has 4 field day ribbons. In how many ways can she display all four of them on her wall?

Try this one Kelly has 4 field day ribbons. In how many ways can she display all four of them on her wall? 4 x 3 x 2 x 1 = 24

Permutation – Permutation – 3. A permutation is an arrangement of a set of objects in a particular order. You can use the notation nPr to express the number of permutations of n objects chosen r at a time. 3. A permutation is an arrangement of a set of objects in a particular order. You can use the notation nPr to express the number of permutations of n objects chosen r at a time. Example – In a bag, there are 10 blocks that are all different colors. In how many different ways can you select 5 blocks? Example – In a bag, there are 10 blocks that are all different colors. In how many different ways can you select 5 blocks? 10 P 5 = 10 x 9 x 8 x 7 x 6 = 30,240 ways 10 P 5 = 10 x 9 x 8 x 7 x 6 = 30,240 ways

Try this one Try this one Find the value of the expression. 6 P 3

Try this one Try this one Find the value of the expression. 6 P 3 6 x 5 x 4 = 120