if two of the 4 expressions x + y , x + 5 y , x - y , 5 x + y are chosen at random , what is the probability that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?  Select:
A) 1 / 2
B) 1 / 3
C) 1 / 4
D) 1 / 5
E) 1 / 6

Rationale: there are total 4 c 2 = 64 c 2 = 6 ways to choose 2 equations out of 4 at random . we want the product of 2 equations in format x 2 − ( by ) 2 x 2 − ( by ) 2 , where b is a constant coefficient of term y 2 y 2 . also note equation does not contain any xyxy term . there are only 2 equations , ( x + y ) & ( x - y ) which gives the product x 2 − y 2 x 2 − y 2 . product of all other equations will contain term xyxy so answer = 1 / 6 ans : e
Answer: E