If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability that thier product will be the form of x^2- (by)^2, where b is an integer?
looks like 1/6.
You basically need to pick both x+y and x-y. Those are the only two that will satisfy the stem.
Since we know there is only 1 way for this to happen (when you don't consider order choosing x+y and x-y is the same as choosing x-y and x+y), we need to figure out how many ways you can chose 2 equations (without order being important).
4C2 = 4!/(2!*(4-2)!) = 6
Since there's 1 way it can work, and 6 possibilities, we have 1/6.
