Permutations_and_Combinations-5.5-Notes

Permutations_and_Combinations-5.5-Notes - 9/23/2009 The...

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9/23/2009 1 Permutations and Combinations (5.5) 1 2 The ideas used in this section are very similar to what we have used before. There will be another consideration that needs to be made when we discuss combinations – namely, that sometimes order does not matter when making a selection. 3 Example (5.5.25): How many ways are there to choose first, second, and third prizes in an art contest with 15 entrants? 1st 2nd 3rd 15 choices 14 choices 13 choices = 2730 ways × × 4 What we have computed here is called a permutation . We have a pool of 15 people, and we have selected 3 people from that pool. Here the order DOES matter! First place, second place, and third place are different!
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9/23/2009 2 5 The symbol for this is and it is pronounced “ n permute r .” This is the number of ways that r objects can be selected from a collection of n objects when order is important. The formula is 6 Just in case you forgot what factorial is, the definition is So, for example, 7 In the example above, we chose 3 objects from a collection of 15 (where order mattered), and so that was 8 Example: Given the four cards pictured here how many two card hands can be made? Let’s do the usual: First card: Second card: 4 choices 3 choices ×
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9/23/2009 3 9 So, it appears as though there are 12 possibilities, but let’s look at them more closely:
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This note was uploaded on 02/16/2011 for the course MAT 194 taught by Professor Staff during the Fall '08 term at Syracuse.

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Permutations_and_Combinations-5.5-Notes - 9/23/2009 The...

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