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 AP is 
.
Statement -2 : If the four chosen numbers form an AP, then the set of all possible values of
common difference is {±1, ±2, ±3, ±4, ±5}
Text Solution
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Sol. Statement-1 Total ways = 20 C 4
number of AP's of common difference 1 is = 17
number of AP's of common difference 2 is = 14
number of AP's of common difference 3 is = 11
number of AP's of common difference 4 is = 8
number of AP's of common difference 5 is = 5
number of AP's of common difference 6 is = 2
total = 57
probability = 
= 
Statement-2 common difference can be ± 6 , so statement -2 is false. Hence correct option is
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