Probability that their product (GMAT PREP 1)

Hi,

Using the combination formula, we will know how many groupings of 2 of these 4 expression we can have:4!/(4-2)!2!=6

So, now, let's see how many of these 6 combinations are of the form of (x^2)-[(by)^2], which is (x+by)(x-by)...

(x+y)(x+5y): it's not of the form of (x+by)(x-by), so NO
(x+y)(x-y): it is of the form of (x+by)(x-by), so YES
(x+y)(5x-y): not of the form of (x+by)(x-by), so NO
(x+5y)(x-y): not of the form of (x+by)(x-by), so NO
(x+5y)(5x-y): not of the form of (x+by)(x-by), so NO
(x-y)(5x-y): not of the form of (x+by)(x-by), so NO

So only one of these 6 combinations is of the form of (x+by)(x-by)...

Therefore, the correct answer is E.