Question

Three numbers are selected randomly between $1$ to $20$. Then the probability that they are consecutive numbers will be

• A. $\frac{7}{190}$
• B. $\frac{3}{190}$
• C. $\frac{5}{190}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$\frac{3}{190}$

Number of sample space for selecting three numbers between $1$ to $20{=}^{20}{C}_3$
Number of ways that they are consecutive numbers $=18\left\{\right(1,2,3\left)\right(2,3,4\left)\right(3,4,5)\dots \dots ,(18,19,20\left)\right\}$
$\therefore$ Required probability
$=\frac{18}{{}^{20}{C}_3}=\frac{18\times 3\times 2}{20\times 19\times 18}$

$=\frac{3}{190}$