Question:
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:
Correct Option: , 3
Solution:
For an A.P. $2 b=a+c$ (even), so both $a$ and $c$ even
numbers or odd numbers from given numbers and $b$ number will be fixed automatically.
Required probability $=\frac{{ }^{6} C_{2}+{ }^{5} C_{2}}{{ }^{11} C_{3}}=\frac{25}{165}=\frac{5}{33}$