MAT 146 Midterm: MAT 146 Spring 18 Exam
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Do not turn this page until told to. Each of the 4 problems is worth 30 points. 4 for o ce use: let cn the number of ways to arrange n distinct cards in a row of piles. Note: the number of piles and their sizes can be any positive numbers. The order of the piles in the row matters, as well as the order of cards in each pile. Examples: c1 = 1, c2 = 4. (a) find, by any method, the exponential generating function of cn. (b) find, by any method, a simple formula for cn. Examples: f3,1 = 0, f3,2 = 1, f3,3 = 1, f8,4 = 2. Write in a simple form the generating function f (x, y) = P k=0 fn,kxnyk (b) let gn = the number of ways to pay with any number of coins.
