Mathematics - Probability Question with Solution | TestHub

$n(s)={}^{3n}{C}_2$

Let $A_0=\{3,6,9\dots \dots \dots 3n\}$

$A_1=\{1,4,7\dots \dots \dots 3n-2\}$

$A_2=\{5,8,11\dots \dots \dots .3n-1\}$

( $x^2-y^2$ ) divisible by 3 . If both $\mathrm{x},\mathrm{y}$ should come

from $A_0$ or $A_1$ or $A_2$ or one is from $A_1$ and other from $A_2$

$$\begin{array}{rlr}& n(E)=3^n{C}_2+{}^n{C}_1+{}^n{C}_1=\frac{n}{2}(5n-3)& P(E)=\frac{5n-3}{3(3n-1)}\end{array}$$