Out of 11 consecutive natural numbers, three are selected at random.

Question

Out of 11 consecutive natural numbers, three are selected at random. Find the probability they are in A.P. with positive common difference.

Accepted Answer

For an A.P., $2b=a+c$ requires $a,c$ both odd or both even (6 even, 5 odd among 11 numbers).

$$P = \frac{{}^6C_2+{}^5C_2}{{}^{11}C_3} = \frac{15+10}{165}=\frac{25}{165}=\frac{5}{33}$$

Solutions · 1