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Unformatted text preview: since the balls with the same color are in fact indistinguishable. Dividing by these repeated patterns gives n ! r !( n-r )! , gives the unique number of permutations. Problem 5 (the number of binary vectors who’s sum is greater than k ) To have the sum evaluate to exactly k , we must select at k components from the vector x to have the value one. Since there are n components in the vector x , this can be done in ± n k ² ways. To have the sum exactly equal k + 1 we must select k + 1 components from x to have a value one. This can be done in ± n k + 1 ² ways. Continuing this pattern we see that the number of binary vectors x that satisfy n ³ i =1 x i ≥ k...
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This note was uploaded on 02/25/2011 for the course STAT 418 taught by Professor G.jogeshbabu during the Winter '08 term at Pennsylvania State University, University Park.
- Winter '08