1 / 9

Combinations & Permutations

Combinations & Permutations. Essentials: Permutations & Combinations (So that’s how we determine the number of possible samples!). Definitions: Permutation; Factorial; Combination. What a Factorial is and how to use it.

aquila
Download Presentation

Combinations & Permutations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Combinations & Permutations

  2. Essentials:Permutations & Combinations(So that’s how we determine the number of possible samples!) • Definitions: Permutation; Factorial; Combination. • What a Factorial is and how to use it. • Ability to determine the number of permutations or combinations resulting from a stated situation. • Extras here: Tree diagrams & the multiplication rule.

  3. A Tree Diagram systematically lists all possible ways a sequence of events can occur. Advantage: Visual display of sequential events. Disadvantage: Only practical where the number of choices are small. Example: What are the possible results of flipping a coin twice? Tree Diagrams H H T H T T Results: HH HT TH TT

  4. Multiplication Rule (events independent) • In a sequence of n events in which the first event has k1 possibilities, the second event k2, etc. (to kn), the total number of possibilities is k1* k2* …* kn-1* kn. • Example 1: • What are the possible results of flipping a coin twice? • Answer: 2 * 2 = 4 • The Multiplication Rule replaces tree diagrams of any size. Consider the tree diagram that would result from the following example. • Example 2: • What are the dinner possibilities if there are 10 beverages, 6 appetizers, 11 entrees, and 8 desserts? • Answer: 10 * 6 * 11 * 8 = 5,280 dinner possibilities.

  5. Factorials • The Factorial of a number is the multiplication of that number by every smaller number down to 1. • The Factorial Notation is n!, where n represents the number and the “!” indicates the factorial process. • Note the following: By definition 0! = 1 • Example: 8! = 8 * 7 *6 * 5 * 4 * 3 * 2 *1 = 40,320

  6. Permutations • A Permutation is an arrangement of n objects in a specific order using r objects at a time.

  7. Permutations: Examples • Example: A news program has time to present 2 of four available news stories. How many ways can the evening news be set up? • Checking the process: • If we let A, B, C, D represent the four shows, then the possible show orders would be: • AB BA CA DA • AC BC CB DB • AD BD CD DC • Twelve (12) possible presentations where order matters.

  8. Combinations • A combination is the selection of r objects from n objects without regard to order.

  9. Combinations: Examples • Example: A news program has time to present 2 of four available news stories. How many different sets of stories can be presented on the evening news? • Checking the process: • If we let A, B, C, D represent the four shows, then the possible show orders would be: • AB BA CA DA • AC BC CB DB • AD BD CD DC • However, AB and BA represent the presentation of the same two stories. If order does not matter, one of these two may be deleted. Repeating the process results in: AB, AC, AD, BC, BD, CD, • Six (6) different presentations where order does not matter.

More Related