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4203-mid1-review - (b ±or all positive integers n the...

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MAD 4203, Fall 2010 — Some review problems for Midterm #1 These are the problems from Midterm #1 in Fall 2009. 1 A student wants to work exactly 20 days in December, but wants to have at least one of December 25 and December 31 off. In how many ways can the student schedule her 20 workdays? 2 True or False? Explain your answer. (a) The number of three-digit positive integers in which the sum of the digits is even is 450. (b) For all positive integers
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Unformatted text preview: (b) ±or all positive integers n , the integer n 3 + 5 n is divisible by 6. (c) If each of ten people donate money for a cause, each a whole, 2-digit dollar amount, then it is always possible to ²nd two disjoint subsets A and B of these people so that the total contributions of A and B are equal. 3 Prove that for all positive integers n , we have n s k =0 p n k P 2 k ( n-k ) = n 2 p 2 n-2 n-2 P ....
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