Social Choice_Lecture 7b_CountingII

Social Choice_Lecture 7b_CountingII - Math Preliminaries...

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Math Preliminaries: More Counting Matt Van Essen University of Alabama Van Essen (U of A) Counting 1 / 7
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Counting Suppose 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? Well for this sized group we can easily enumerate the groups: AB , AC , AD , AE , BC , BD , BE , CD , CE , DE counting the groups there are 10 di/erent ways. For larger problems enumerating to count is not wise! Fortunately there are some math tricks to help us. Van Essen (U of A) Counting 2 / 7
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Counting In general, if we start with n objects and ask how many ways can we choose k of them (where k is between 1 and n ), then the following notation is used: ° n k ± In particular, ( n k ) referes to the number of distinct ways we can choose exactly k objects from a collection of exactly n objects. Van Essen (U of A) Counting 3 / 7
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Counting Even better, there is a handy formula for computing ( n k ) which follows from the multiplication principle we derived earlier.
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