Four numbers are chosen at random (without replacement) from the set{1, 2, 3, ....., 20}.Statement-1:The probability that the chosen numbers whenarranged in some order will form an APIs `1/(85)`.Statement-2:If the four chosen numbers from an AP, then the setof all possible values of common difference is {1, 2, 3, 4, 5}.

Four numbers are chosen at random (without replacement) from the set{1

1.	Four numbers are chosen at random (without replacement) from the set{1, 2, 3, ....., 20}.Statement-1:The probability that the chosen numbers whenarranged in some order will form an APIs `1/(85)`.Statement-2:If the four chosen numbers from an AP, then the setof all possible values of common difference is {1, 2, 3, 4, 5}.
Answer» `a= 1 ; d= 1; {1,2,3,4,17,18,19,20,17}` `d= 2 ; {1,3,5,7, 14,16,18,20,14}` `d=3 ; {1,4,7,10,11,14,17,20}` P(4 are in AP) = `(17+2)/2 xx6/(.^20C_4) = 57/(.^20C_4)` `= (57 xx 4 xx 3 xx 2)/(20 xx 19 xx 18 xx 17) = 1/85` option 2 is correct

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