Build a generating function for a, in the following procedures. Remember to state which coefficient solves the initial problem. You do not need to calculate the coefficient, but I recommend writing expand g(r) in Wolfram Alpha for at least one of the generating functions g(r); doing so will provide further intuition. Consider each of the following separately: (a) How many ways are there to distribute 25 identical pieces of candy to 3 adults and 10 children so that each adult gets at most one piece (remember that people are considered to be distinct)? (b) How many ways are there to distribute r cents, using 100 pennies, 20 nickels, and 10 dimes? Hint: it is important to note that each penny = 1 cent, each nickel = 5 cents, and each dime = 10 cents. (c) How many ways are there to observe a sum of 18 when 7 distinct dice are rolled? (d) How many ways are there to distribute 30 identical homework assignments to 5 graders so that each grader gets at least 4, but no more than 8 homework assignments?