15_Counting - Permutations 10/13/11 An ordered arrangement...

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Permutations 10/13/11 An ordered arrangement of r elements out of n distinct elements is called an r-permutation. For the above problem, we counted 3-permutations of 3 distinct elements: Example : If the number of available students is 5 and the line should have three students, then the number of ways to form a line is
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right hand side Example : How many ways are there to select three -- first, second, third place -- winners out of 100? Problem 2 . S={a,b,c,d,e,f,g}. |S|=7.
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2'. Example 7 . How many ways can the letters A, B, C, D, E, F, G, H be permuted to form 8-letter strings that contain the substring ABC. Alternate solution:
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Combinations
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Theorem 2 An r-combination of the elements of a set is an unordered selection of r elements from the Set. Example 11 . The number of 5-card poker hands from a standard deck of 52 cards is The number of 47-card poker hands from a standard deck of cards is
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Corollary 2 Algebraic manipulation Combinatorial proof : Counting arguments are used to show that both sides of an identity count the same objects in different ways.
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15_Counting - Permutations 10/13/11 An ordered arrangement...

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