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Question:

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 1/85. Statement-2: If the four chosen numbers form an A.P., then the set of all possible values of common difference is ±1, ±2, ±3, ±4, ±5.

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Statement-1 is true, Statement-2 is false

Statement-1 is false, Statement-2 is true

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

Solution:

N(S) = 20C4
Statement-1: common difference is 1; total number of cases = 17
common difference is 2; total number of cases = 14
common difference is 3; total number of cases = 11
common difference is 4; total number of cases = 8
common difference is 5; total number of cases = 5
common difference is 6; total number of cases = 2
Probability = (17 + 14 + 11 + 8 + 5 + 2) / 20C4 = 57/4845 = 1/85.