Q116 / 160 · WBJEE 2009 · Mathematics

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

A
$\frac{1}{190}$
B
$\frac{1}{120}$
Correct answer
C
$\frac{3}{190}$
D
$\frac{5}{190}$

Solution

Hints: Total number of cases ; ${ }^{20} \mathrm{C}_3=\frac{20 \times 19 \times 18}{2 \times 3}=20 \times 19 \times 3=1140$ Total number of favourable cases $=18$ $\therefore$ Required probability $=\frac{18}{1140}=\frac{3}{190}$

Hence, the correct answer is option: 'C'.

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