Question

Two numbers x and y are chosen at random from the set {1,2,3........3n}. The probability that $x^2-y^2$ is divisible by 3 is

Answer 1

$x^2-y^2$ is divisible by 3 if either both $x$ & $y$ are divisible by 3 or if both are not divisible by 3.

$\therefore$ Probability$=\frac{{}^n{C}_2{+}^{2n}{C}_2}{{}^{3n}{C}_2}$