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Unformatted text preview: x 4 ? 5. Chapter 1 Theoretical Exercise 18. 6. Two friends go for dinner at a restaurant which has m items on the menu. Each order one item (which may be the same), and if they are still hungry they may then order any selection of items that have not yet been ordered to share. By counting how many diFerent orders they can make, prove the identity: m X k =1 k 2 m k = m + 1 2 2 m1 Bonus Question: In how many ways can m identical red balls, m identical blue balls, and m identical green balls be distributed amongst boxes labelled 1 , 2 , 3, so that each box gets exactly m balls? * or full marks, your answer must be in the form of a simple formula which does not include a series. Id strongly suggest drawing the solutions for the m = 2 case so that you can check if your formula gives the correct answer. (I did NOT get this right on the rst try!)...
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 Spring '09
 M.Tao
 Math, Probability

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