Do Problems: Problem 1: 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. (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? (b). The number of ways to give a total of r cents, using one dollar worth of pennies, one dollar worth of nickels and one dollar worth of dimes. (c). How many ways can we get a sum of 18 when 7 distinct dice are rolled? (d). How many ways are there to distribute 30 identical homeworks to 5 graders so that each grader gets at least 4 but no more than 8 homeworks? Problem 2: (a). What is the coefficient of x40 in the expansion of (23 + 24 + 25 + 26 + 27 + ... )4? (b). What is the coefficient of 230 in the expansion of (a + x2 + 23 + 24 + 25 + 26) 10? Problem 22 - Section 6.2