Question

The number of distinct rational numbers $n$ such that $0<n<1$ and $n=\frac{p}{q},$ where $p,q\in 1,2,3,4,5,6$ is

• A. $15$
• B. $13$
• C. $12$
• D. $11$

Answer 1

The correct option is D $11$

Out of the given $6$ digits, $2$ digits can be selected in ${}^6{C}_2$ ways and they can be arranged in only one way to satisfy the give condition.

Out of these ways $\left(\frac{1}{2},\frac{2}{4},\frac{3}{6}\right)$,$\left(\frac{2}{3},\frac{4}{6}\right)$ and $\left(\frac{1}{3},\frac{2}{6}\right)$ represent same number.
$\therefore$ No. of numbers $=15-4=11$.