A committee of 5 is to be selected from a group of 6 men and 9 women. Suppose the selection is made randomly. (a) What is the probability that the committee consists of 3 men and 2 women? (b) What is the probability that the committee consists of at least two women?

A classroom contains 10 girls and 8 boys. You need to randomly select some of the students for testing. You cannot select the same student twice.(a) What is the probability of randomly selecting a girl?(b) If you randomly selected two students, what is the probability of selecting two boys?(c) You randomly select three students. What is the probability that the third student you select is a girl, given the first two were boys?(d) What is the most likely outcome when randomly choosing two students: selecting two of the same gender (2 boys or 2 girls), or choosing a boy-girl pair? Explain your reasoning.

Assume that a class has 20 students, in which the students are arranged in a line by the teacher randomly. What is the probability that the 4 smallest students in the line will be next to one another?