A college cricket team with $11$ players consists of $4$ batsman, $3$ all-rounders, $3$ bowlers and $1$ wicket keeper. $3$ players are selected randomly. Find the probability that the selection contains a batsman, a bowler and an all-rounder.
- $\dfrac{12}{60} \\$
- $\dfrac{13}{25} \\$
- $\dfrac{12}{55} \\$
- $\dfrac{104}{165}$