If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability R that their product will be of the form of x^2-(by)^2, where b is an integer?  Choose the most appropriate option:
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) R=1/6
Only (X+y)(x-y) pair will give the form x^2-(by)^2   The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability R= 1/12 * 2 = 1/6   Ans R=1/6
<result>E</result>
If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability R that their product will be of the form of x^2-(by)^2, where b is an integer?