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ClassNotes-Math-Factorials

ClassNotes-Math-Factorials - Sven Thommesen 2011 Math...

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1 © Sven Thommesen 2011 Math: Factorials, combinations, permutations (Needed in Ch 4) [Edited 09/23/08] [This note merely defines some mathematical concepts we’ll need. The chapter notes will tell you when and how to use these concepts.] In order to discuss how to calculate probability in various contexts, we need to define the following new mathematical concepts: (a) FACTORIALS The factorial is used to calculate the answer to the following question: How many different sequences, or permutations , can we form from a group of N items? Definition: the factorial N! = 1 2 3... 1 N i N i    and we define 0! = 1 For example: 2! = 2 x 1 = 2 5! = 5 x 4 x 3 x 2 x 1 = 120 For example, how many different ways can we line up 4 cars in a row? The answer is: 4! = 4 x 3 x 2 x 1 = 24 ways. To see how: for the first spot in the lineup we can pick either of the 4 different cars. For the second spot, we have only 3 left to choose from. For the third spot, there are 2 left. And for the last spot, there’s only one car left, since the other 3 have been taken. So the number of possible ways we
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