Social Choice_Lecture 7b_CountingII

Arrange these k objects in some order arrange the

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Unformatted text preview: ge these k objects in some order, Arrange the remaining n k objects in some order. n Step 1 can be done in (k ) ways, Step 2 can be done in k ! ways, and Step 3 can be done in (n k )! ways. We know the number of possible arrangements is n !, but, by the n multiplication principle n ! = (k )k !(n k )! n Solving for (k ) gives us the desired conclusion n k Van Essen (U of A) = n! k ! (n k ) ! Counting 5/7 Counting Example Supose we have 5 people {A, B, C, D, E} and are interested in putting them in groups of 2. How many di¤erent groups of 2 can we form? Van Essen (U of A) Counting 6/7 Counting Example Supose we have 5 people {A, B, C, D, E} and are interested in putting them in groups of 2. How many di¤erent groups of 2 can we form? Answer: 54 5 5! = = 10 = 2 2!3! 2 Van Essen (U of A) Counting 7/7...
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This note was uploaded on 04/08/2014 for the course ECON 497 taught by Professor Vanessen during the Spring '12 term at Alabama.

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