1 / 9

Alg II - Ch#10 Section 1 & 2 Counting Methods Factorial Permutations Combinations

Alg II - Ch#10 Section 1 & 2 Counting Methods Factorial Permutations Combinations. Fundamental Counting Principle. If one event can occur in m ways and another event can occur in n ways, Then the number of ways that both events can occur is m * n. Example #2

nizana
Télécharger la présentation

Alg II - Ch#10 Section 1 & 2 Counting Methods Factorial Permutations Combinations

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. Alg II - Ch#10 Section 1 & 2 Counting Methods Factorial Permutations Combinations

  2. Fundamental Counting Principle If one event can occur in m ways and another event can occur in n ways, Then the number of ways that both events can occur is m * n.

  3. Example #2 You want to frame a picture. The frames come in 12 different Styles. Each Style comes in 55 different colors. You want a blue mat board, which is available in 11 different Shades of blue. How many ways can you frame the picture? ___ * ___ * ___ = ____

  4. Permutations - An ordering of n objects is a permutation of the objects For example, There are 6 permutations of the letters A,B,C: ABC ACB BAC BCA CAB CBA 3 possible choices for the 1st letter, 2 choices for the second letter and 1 choice for the 3rd letter. Thus the number of Permutations is 3 . 2 . 1 = 6

  5. Factorial The Expression 3 . 2 . 1 can also be written as 3!. The symbol ! Is the factorial symbol and 3! is called 3 Factorial

  6. Example #3 The standard configuration or a Texas license plate is 1 letter followed by 2 digits followed by 3 letters. a. How many different license plates are possible if letters and digits can be repeated? ___ * ___ * ___ * ___ * ___* ___ = ____ b. How many different license plates are possible if letters and digits can not be repeated? ___ * ___ * ___ * ___ * ___ * ___ = ____

  7. Example #4 Ten teams are competing in the final round of the Olympic four-person bobsledding competition. a. In how many ways can the teams finish the competition? b. In how many different ways can 3 of bobsledding teams finish first, second and third?

  8. Permutations of n objects Taken r at a time. The permutations of r objects taken from a group of n distinct objects is denoted by nPr= Example 5 – Your are burning a demo CD or your band. Your band has 12 songs stored on your computer. In how many ways can you burn 4 of the 12 songs onto the CD? 12P4 =

  9. Permutations with Repetitions . The number of distinguishable permutations of n objects where one object is repeated s1 times, another is repeated s2 times and so on is: Example 6 – Find the number of distinguishable permutations of the letters in (a) MIAMI P =

More Related