Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:

For an A.P ,2b= a + c ( even), so both a and c even numbers or

odd numbers from given numbers and b number will be fixed

automatically required probability  $=\frac{{ }^6{c}_2{+}^5{c}_2}{{ }^{11}{c}_3}=\frac{25}{165}=\frac{5}{33}$