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Lesson # 64 – 65 Notes Permutations and Combinations

Lesson # 64 – 65 Notes Permutations and Combinations. 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.

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Lesson # 64 – 65 Notes Permutations and Combinations

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  1. Lesson # 64 – 65 NotesPermutations and Combinations 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 2 x 6 = 12

  2. 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?

  3. 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 3x2x3x 3 =54choices

  4. 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

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

  6. 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

  7. Permutation – 3. A permutation is an arrangement of a set of objects in a particular order. You can use the notation nPrto 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? • 10P5 = 10 x 9 x 8 x 7 x 6 = 30,240 ways

  8. Try this one  Find the value of the expression. 6P3

  9. Try this one  Find the value of the expression. 6P3 6 x 5 x 4 = 120

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