Four numbers are chosen at random (without replacement) from the set $\{1, 2, 3, ..., 20\}$.
Statement-$1$: The probability that the chosen numbers when arranged in some order will form an $A.P.$ is $\frac{1}{85}$.
Statement-$2$: If the four chosen numbers form an $A.P.$,then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6\}$.

• A
  Statement-$1$ is true,Statement-$2$ is true; Statement-$2$ is a correct explanation for Statement-$1$.
• B
  Statement-$1$ is true,Statement-$2$ is true; Statement-$2$ is not a correct explanation for Statement-$1$.
• C
  Statement-$1$ is true,Statement-$2$ is false.
• D
  Statement-$1$ is false,Statement-$2$ is true.