Senate Committees. The U.S. Senate consists of 100 senators, 2 from each state. A committee consisting of 5 senators is to be formed. a. How many different committees are possible?b. How many are possible if no state may have more than 1 senator on the committee?c. If the committee is selected at random from all 100 senators, what is the probability that no state will have both of its senators on the committee?

Nine people apply for three jobs. Five of them are women, four of them are men. 1. If three people selected at random, what is a probability that all three are woman?(Give your answer as a fraction, you do not need to simplify) 2.lf three people selected at random, what is a probability that only one is woman?(Give your answer as a fraction, you do not need to simplify) 3. If three people selected at random, what is a probability that at least two are men?(Give your answer as a fraction, you do not need to simplify) 4.lf three people selected at random, what is a probability that at most one is a man?(Give your answer as a fraction, you do not need to simplify)

1. A bag contains 7 green marbles, 2 white marbles, and 3 red marbles. A marble is removed and then placed back in the bag, and a second marble is picked. What is the probability of drawing a green marble and then a red marble? (Enter your probability as a fraction.) 2. A large box of vegetables contains 3 tomatoes, 4 heads of lettuce, and 8 onions. A vegetable is chosen at random and then replaced in the box, and a second vegetable is picked. What is the probability of choosing a tomato and then an onion? (Enter your probability as a fraction.)

A group consists of five men and six women. Five people are selected to attend a conference. a. In how many ways can five people be selected from this group of eleven? b. In how many ways can five women be selected from the six women? c. Find the probability that the selected group will consist of all women. a. The number of ways to select five people from the group of eleven is b. The number of ways to select five women from the group of six women is c. The probability is. (Type an integer or a simplified fraction.) G