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Unformatted text preview: n = 36. Q4. Let d be a positive integer. Show that among any group of d + 1 (not necessary consecutive) integers there are two with exactly the same remainder when they are divided by d . Answer Any number i when divided by d gives a remainder r where 0 r < d . Since we have d + 1 integers and d possible remainders, there will be at least d +1 d = 2 integers with the same remainder. Q5. How many subsets with more than two elements does a set with 15 elements have? Answer The total number of subsets = 2 15 . The number of subsets with 0 element is 1, with 1 element is 15, and with 2 elements is C(15 , 2) = (15 14) / 2! = 105. Therefore, the number of subsets with more than two elements = 2 15 (1 + 15 + 105) = 32 , 647. 1...
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This homework help was uploaded on 04/19/2008 for the course CS 182 taught by Professor W.szpankowski during the Fall '08 term at Purdue University-West Lafayette.
- Fall '08