Unformatted text preview: 1. Find the coeﬃcient of x 12 in 1 (1+ x ) 8 2. Find a generating function for the number of solutions in nonnegative integers to x 1 + x 2 + x 3 = k where 3 ≤ x 1 , 2 ≤ x 2 ≤ 10 , 5 ≤ x 3 . What if you add the requirement that x 3 is even? 3. Find a generating function for the number of ways to make n cents using pennies, nickels, dimes, and quarters, where the order of the coins doesn’t matter. Use this to ﬁnd the number of ways to make 10 cents....
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This note was uploaded on 02/06/2012 for the course MATHEMATIC 55 taught by Professor Robbayer during the Summer '09 term at Berkeley.
 Summer '09
 RobBayer
 Math

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