Out of 11 consecutive natural numbers


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:

  1. (1) $\frac{15}{101}$

  2. (2) $\frac{5}{101}$

  3. (3) $\frac{5}{33}$

  4. (4) $\frac{10}{99}$

Correct Option: , 3


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 $=\frac{{ }^{6} C_{2}+{ }^{5} C_{2}}{{ }^{11} C_{3}}=\frac{25}{165}=\frac{5}{33}$

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