d) Class distinctions revisited One hundred students are taking a class, including fifty women and fifty men. They are randomly assigned to fifty teams of two, and independently, the registrar assigns the students to ten distinct class sections, so that each section has exactly ten students. Find the probability that the first section includes at least one woman. Consider the number of teams with both students assigned to the same section. Find its expected value. Consider the number of women assigned to the first section. Find its expected value and variance. Consider the number of teams in the class with two women students. Find its expected value and variance