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# Assn2 - you select 10 of these balls(the balls of the same...

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1. Determine the rook polynomial of the following board: In how many ways can you place 6 non-taking rooks on this board? In how many ways can you place them on the complementary board? 2. An integer n is an exact power if there exist integers x and y such that y > 1 and n = x y ; for example, 1 = 1 2 , 4 = 2 2 , 8 = 2 3 and 9 = 3 2 are all exact powers that are smaller than 10. How many integers between 1 and 1000 are exact powers? 3. You are given 3 red, 4 green and 6 blue balls. In how many ways can
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Unformatted text preview: you select 10 of these balls (the balls of the same color are indistin-guishable)? 4. Determine the coeFcient of x 50 in the power series corresponding to the function 1-x 20 1-2 x . 5. Simplify p-2 k P and p-1 / 2 k P to expressions using only “ordinary” binomial coeFcients (i.e., p a b P , where a and b are nonnegative integers)....
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