PSL4#31

This is analogous to the situation of  distributing 7 distinct balls into 3 distinct boxes such that every box  must contain at least one ball

The total arrangements are given by :

(Stirling number of the second kind) (7, 3)  * 3!  =

S₂ (7,3) * 3!  =

301  * 3!  =

301 * 6  =

1806