355w2003_midterm - Mth 355 Midterm Bent Petersen...

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Mth 355 Midterm Name: ID: Bent Petersen 355w2003_midterm.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). Consider an m × n rectangular grid. How many routes are there from the lower left corner to the upper right corner if we allow only travel to the right or upward? Hint: Each route may be associated with a string consisting of m U’s and n R’s where R indicates a right step and U indicates an upward step. Problem 2. (20 points). If we toss a fair coin 20 times we can record the outcome as a sequence of H’s (for heads) and T’s (for tails). Clearly there are 2 20 possible strings. What fraction of these strings contain exactly 10 H’s? Problem 3. (20 points). Let X be a set of cardinality 12 and let Y be a set of cardinality 5. The number of partitions of X into 5 non-empty subsets is S (12 , 5) =1,379,400. How many epimorphisms f : X Y are there? Problem 4.
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This note was uploaded on 02/11/2012 for the course MTH 141, 142, taught by Professor Mcallister during the Spring '08 term at SUNY Empire State.

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355w2003_midterm - Mth 355 Midterm Bent Petersen...

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