In a school annual day function a variety programme was organised. It was planned that there would be $3$ short plays, $6$ recitals and $4$ dance programmes. However, the chief guest invited for the function took much longer time than expected to finish his speech. To finish in time, it was decided that only $2$ short plays, $4$ recitals and $3$ dance programmes would be performed. How many choices were available to them if the programmes can be performed in any order?
