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  1. There are five distinct computer science books, three distinct mathematics books, and two distinct art books. In how many ways can these books be arranged on a shelf if no two of the three mathematics books are together?
  2. There are five distinct computer science books, three distinct mathematics books, and two distinct art books. In how many ways can these books be arranged on a shelf if one of the art books is on the left of all the mathematics books, and the other art book is on the right of all the mathematics books?
  3. The letters ABCDEFGH are to be used to form strings of length 5. How many strings contain the letter A if repetitions are allowed?
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