Two integers $x$ and $y$ are chosen with replacement from the set $(0,1,2$, $\qquad$ 10). The probability that $|x-y| \gt 5$ is

• A

  6/11
• B

  35/121
• Correct answer
  C

  30/121
• D

  25/121

Solution

Probability $=\frac{2 \times \frac{1}{2} \times 5 \times 6}{11 \times 11}=\frac{30}{121}$

Hence, the correct answer is option: 'C'.