Solutions from a student (dragged) 16

Solutions from a student (dragged) 16 - since the balls...

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we have n 1 n 2 n 3 ··· n m total experimental outcomes. Problem 3 (selecting r objects from n ) To select r objects from n ,wew i l lhave n choices for the Frst object, n - 1cho icesforthe second object, n - 2cho ice sfo rtheth i rdob jec t ,e tc . Con t inu ingwew i l lhave n - r +1 choices for the selection of the r -th object. Giving a total of n ( n - 1)( n - 2) ··· ( n - r +1) total choices if the order of selection matters. If it does no tthenw emu s td iv idebythe number of ways to rearrange the r selected objects i.e. r !g iv ing n ( n - 1)( n - 2) ··· ( n - r +1)
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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.

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