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Unformatted text preview: 1. Find the coecient of x 12 in 1 (1+ x ) 8 2. Find a generating function for the number of solutions in non-negative 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 doesnt matter. Use this to nd the number of ways to make 10 cents....
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- Summer '09