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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

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

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  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 =

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