what is the probability that the three runners from team A will finish first, second and third & the three runners from team B will finish fourth, fifth and sixth?

We randomly put blue and red marbles into two boxes. It ends up that the first box has 6 blue marbles and 8 red marbles The second box has 6 blue marbles and 2 red marbles. We randomly pick one box, and randomly pick a marble from it. If the marble we picked was red, what is the probability that we drew from the first box?

A bag contains 8 black marbles, 7 green marbles, 4 white marbles. If one marble is drawn from the bag then replaced, what is the probability of drawing a black marble then a white marble?

a bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. what is the probability of drawing a black and then a red marble out of the bag without replacing the black marble before drawing a red marble?

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.

If a committee of 5 senators are selected from the 100 members of the the U.S. Senate, what is the probability that no 2 committee members are from the same state?

A bag contains 3 red marbles, 5 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be blue?