Question

The probabiltiy of a increasing G.P. being formed, if we select three numbers from the set $\{1,2,3,\cdots ,10\}$ is
(correct answer + 1, wrong answer - 0.25)

• A. $\frac{1}{30}$
• B. $\frac{1}{40}$
• C. $\frac{1}{24}$
• D. $\frac{1}{20}$

Answer 1

The correct option is A $\frac{1}{30}$

$1,2,4;4,6,9;2,4,8;1,3,9$ are $4$ G.P.s
$\therefore$ Required probability$=\frac{4}{{}^{10}{C}_3}=\frac{4}{120}=\frac{1}{30}$