Probability, does the order matter? According to Webster’s New Collegiate Dictionary, a divining rod is “a forked rod believed to indicate [divine] the presence of water or minerals by dipping downward when held over a vein.” To test the claims of a divining rod expert, skeptics bury four cans in the ground, two empty and two filled with water. The expert is led to the four cans and told that two contain water. He uses the divining rod to test each of the four cans and decide which two contain water. a) List the sample space b) If the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water? W = water, E = empty For a) I have, (W1, E1), (W1,E2), (W1,W2), (W2, E1), (W2, E2), (E1, E2), but I'm just wondering if order matters. Is (E1, W1) different from (W1, E1)? b) is it just 1/6?

Everything you have said is correct, but I want to elaborate a little bit on $b)$. There are four cans, two of which are being chosen essentially at random. There are $$\binom{4}{2} = 6$$ possible choices of two cans, and only one of those choices results in two cans of water. Since each pair of cans is equally likely to be chosen, there is a $1/6$ probability that the two cans containing water are chosen.