Question

Three numbers are chosen at random from $1$ to $20$. The probability that they are consecutive is

• A. $\frac{1}{190}$
• B. $\frac{1}{120}$
• C. $\frac{3}{190}$
• D. $\frac{5}{190}$

Answer 1

The correct option is C $\frac{3}{190}$

The total number of favourable cases, $n\left(E\right)=18$
The total number of cases, $n\left(S\right){=}^{20}{C}_3$
$=\frac{20\times 19\times 18}{3\times 2\times 1}=1140$
$\therefore$ Required probability $=\frac{18}{1140}=\frac{3}{190}$