( Discrete Math )Please answer the questions in the attachment and providing working out on paper

8. Consider the set of six sided die where one dice has the numbers 1, 3, 4, 5, 6, 8 and the other has the numbers 1, 2, 2, 3, 3, 4 (see gure). If these two die are rolled at the same time we'll investigate the possible sums and their frequen- cies in two ways: by direct enumeration in (a) and (b) below, and by using generating functions in (c) and ((1) below. (a) Determine the numbers which can occur as the sum of rolling these two dice. (b) For each number in (a) determine the number of possible ways this sum could be rolled. From this information, write down the generating polynomial D(:r) for the sum when rolling these two die. (c) Now, write down the generating polynomial D1(:r) for the rst dice, and 13201:) for the second dice. (d) Verily that D1(;r) - D2(:r) = D(:r) by multiplying the two polynomials in part (c)