Social Choice_Lecture 7b_CountingII

Van essen u of a counting 37 counting n even better

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Unformatted text preview: ssen (U of A) Counting 3/7 Counting n Even better, there is a handy formula for computing (k ) which follows from the multiplication principle we derived earlier. Theorem For 1 k n (and the convention that 0! = 1), the following holds: n k Van Essen (U of A) = n! . k ! (n k ) ! Counting 4/7 Proof of the theorem First, recall that the number of ways to arrange n objects is n !. With k …xed, we can think about each such arrangement of the n objects as being “built” be the following three step process: 1 2 3 Choose k of the objects to be the initial “block.” Arran...
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