You are given the set of letters {A, B, C, D, E}. What is the probability that in a random five-letter string (in which each letter appears exactly once, and with all such strings equally likely) the letters A and B are next to each other?

There are 7 councilors in the Ames City council. Three of them are female. Suppose they need to select two councilors for a committee. Which expression is computing the probability that if both councilors are selected at random, both will be female? a. None of the other answers is correct. b. 2C3 / 2C7 c. 3/7 d. None of the other answers is correct. e. 3C2 / 7C2 f. 3C2 / 7C3

Eli has a jar full of marbles. In the jar there are 1818 blue​ marbles, 1010 red marbles and 1111 purple marbles.   a. She selects a marble at random from the jar. She does not replace the marble. She selects a second marble from the jar. What is the probability that the second marble is red given that the 1st marble was also​ red? What is the correct interpretation of this​ question?

A person has two drawers that contain socks. One drawer only has one blue​ sock, one red sock and one white sock in it. The other drawer only has one blue​ sock, one black​ sock, one white​ sock, one green sock and one yellow sock in it.​ (no drawer has a pair of matching​ socks.)   One day the person decided to randomly pick one sock out of each drawer.   a. List the possible selectons they can get. b. Find the probability that they will select a a pair of matching socks. c. Find the probability that their selection will contain a red sock or a green sock.