1 / 7

Brought to you by tutorial services – the math center

PERMUTATIONS AND COMBINATIONS. Brought to you by tutorial services – the math center. Fundamental Counting Principle.

cain
Download Presentation

Brought to you by tutorial services – the math center

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. PERMUTATIONS AND COMBINATIONS Brought to you bytutorial services – the math center

  2. Fundamental Counting Principle If there are n(A) ways in which an event A can occur, and if there are n(B) ways in which a second event B can occur after the first event has occurred, then the two events can occur in n(A) · n(B) ways. Special products such as 4! (4 · 3 · 2 · 1) (or any other constant) frequently occur in counting theory. This symbol is a special notation, known as factorial. Factorial is explained as: For any positive integer n, we define n-factorial, written as n! = n(n - 1)(n - 2)(n - 3)……….. We define 0! =1

  3. Permutation and Combination Formulas • Permutation - The number of possible distinct arrangements of r objects chosen from a set of n objects is called the number of permutations of n objects taken r at a time and it equals: nPr = __n!__ (n – r)!

  4. Permutation and Combination Formulas • ExampleIn how many ways can a president, vice president, secretary, and treasurer be selected from an organization with 20 members? • Solution (the number of arrangements in which 4 people can be selected from a group of 20)n = 20 r = 4 nPr = 20!__ = 20 · 19 · 18 · 17 · 16! = 116,280 (20 - 4)! 16!

  5. Permutation and Combination Formulas • Combination - The number of combinations of n objects taken r at a time is: nCr = ___n!___ r!(n – r)!

  6. Permutation and Combination Formulas • ExampleIn the Texas lottery you choose 6 numbers from 1 though 54. If there is no replacement or repetition of numbers, how many different combinations can you make? • Solutionn = 54 r = 6 • nCr = 54!__ = 54 · 53 · 52 · 51 · 50 · 49 = 25,827,165 • 6! (54-6)! 720

  7. Permutations and Combinations Links • Probability Handout • Probability Workshop

More Related