At a sorority meeting, there are 7 seniors, 4 juniors, and 3 sophomores. If a committee of 6 is to be formed, find the probability that 3 from seniors, 2 from juniors, and 1 from sophomores to be selected.

In a box there are 3 red, 4 blue, and 5 white marbles.  If 3 marbles are selected at random and the colors are noted, find the probability that all are white given that all are the same color.

The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a female.

An undergraduate research committee consisting of 4 people is to be formed form 12 doctoral students and 4 supervisors. Find the probability that the committee will consist of exactly 2 doctoral students.

The mathematics department of a college has 6 male​ professors, 11 female​ professors, 10 male teaching​ assistants, and 12 female teaching assistants. If a person is selected at random from the​ group, find the probability that the selected person is a teaching assistant or a female.