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355w2003_midterm_sample - Mth 355 Midterm Bent Petersen...

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Mth 355 Midterm Name: ID: Bent Petersen 355w2003_midterm_sample.tex Feb 26, 2003 Time: 110 minutes. You may use one 8 . 5 × 11 inch sheet of notes. You may use a calculator. Problem 1. (20 points). How many strings are there of length 12 consisting of 3 A’s, 5 B’s and 4 C’s? Problem 2. (20 points). Let X be a set of cardinality 5 and let Y be a set of cardinality 12. How many monomorphisms f : X Y are there? Problem 3. (20 points). Find the number of solutions in positive integers to the equation x 1 + x 2 + x 3 + x 4 = 42 . Problem 4. (20 points). Find the number of solutions in non-negative integers to the equation x 1 + x 2 + x 3 + x 4 = 42 if x 1 2 and x 2 5. Problem 5. (20 points). Find the number of solutions in non-negative even integers to the equation x 1 + x 2 + x 3 + x 4 = 42 . Problem 6. (20 points). Find the number of solutions in non-negative integers to the equation x 1 + x 2 + x 3 + x 4 = 42 if x 1 and x 2 are even and x 3 and x 4 are odd. Problem 7. (20 points). Find the number of solutions in non-negative integers to the inequality x 1 + x 2 + x 3 + x 4 36 .
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