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

Step-by-step solution

2 b = a + c ⇒ sum of a   &   c is even and b depends on a   &   c Thus, we can not choose all three independently, but we can choose a   &   c Moreover, a   and   c should be both either even or odd as their sum is even. Out of 11 consecutive natural numbers, either five are even and six are odd or six are even and five are odd. Hence, P = 1 2 C 2 5 + C 2 6 C 3 11 + 1 2 C 2 6 + C 2 5 C 3 11 = 5 33