x^2-(by)^2=(x-by)*(x+by) where b is a integer

among x+y; x+5y; x-y; 5x-y the only two expressions that satisfy the equation above are (x-y)*(x+y)=x^2-y^2 where b is uqual to 1.

The probability to get one between (x-y) and (x+y) at first try is 2 over 4 so 1 over 2.

The probability to get the remaining expression between (x-y) and (x+y) out of remaining three expressions is 1 over 3.

Since we want the two events happen simultaneously we have to multiply the two probability, therefore:


1/2*1/3=1/6

Agree