Four numbers are chosen at random

Question:

Four numbers are chosen at random (without replacement) from the set $(1,2,3, \ldots .20)$.

Statement-1 : The probability that the chosen numbers when arranged in some order will form

an $\mathrm{AP}$ is $\frac{1}{85}$

Statement-2 : In the four chosen numbers form an AP, then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5\}$.

 

  1. Statement-1 is true, Statement $-2$ is true; Statement- 2 is a correct explanation for Statement$1 .$

  2. Statement-1 is true, Statement $-2$ is true; Statement- 2 is not a correct explanation for Statement-1.

  3. Statement $-1$ is true, Statement- 2 is false.

  4. Statement-1 is false, Statement $-2$ is true.


Correct Option: 3,

Solution:

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