QUESTION : Justify your answers to the following questions. Clearly indicate your final answer. (a) How many committees of 6 people from a group of 10 men and 12 women contain more women than men? (b) What is the smallest number of students in a class that guarantees that at least 7 of these students celebrate their birthday in the same month? (c) How many numbers, at a minimum, must we randomly select from the elements of the set {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} to be certain that we have chosen two numbers whose sum is 20? (d) Let A = {a, a, b, {a, b}} and B = {, {, {}}}. What is the cardinality of P(A B)? (e) What is the coefficient of x^(-6) in (3x - 4x^(-2))^9? (f) Suppose a graph G has 14 vertices and 28 edges. Also, suppose that all vertices of G have degree 0, 3, or 7. If G has exactly 7 vertices of degree 3, how many isolated vertices does it have? (g) Does there exist a graph (potentially a multigraph) whose degree sequence is 0, 1, 2, 3, 4, 5, 5?