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Unformatted text preview: (500 isn't cubefree, so it doesn't matter if we say less than 500 or less than or equal to 500, by the way.) A. To get the cubefree ones, we throw away the ones divisible by 2^3, 3^3, 5^3, and 7^3. Then we have to add one thing back: the one number less than 500 that's divisible by two of these, 2^3 and 3^3. So it's 499  floor(499/2^3)  floor(499/3^3)  floor(499/5^3)  floor(499/7^3) + 1. (If you want, that's 499  62  55  3  1 + 1.) 3. How many ways can 0,1,2,3,4,5,6,7,8,9 be rearranged so that no even digit is in its final position? A. We basically follow the derangement derivation, and get 10!  (5 choose 1) 9! + (5 choose 2) 8!  (5 choose 3) 7! + (5 choose 4) 6!  (5 choose 5) 5!....
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 Spring '08
 STRAIN
 Probability

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