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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.

  1. $\dfrac{12}{60} \\$
  2. $\dfrac{13}{25} \\$
  3. $\dfrac{12}{55} \\$
  4. $\dfrac{104}{165}$
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