This is an extension to # 2747 and can be solved in a similar way.

We can model these $17$ people using $17$ points and the $3$ languages using $3$ different colored edges connecting these points. Then the to-be-proved claim is equivalent to show that there must exist a triangle made up with same colored edges.

Pick up any point, there will be $16$ edges starting from this point. By the pigeonhole principle, at least $6$ of them will share the same color. Then if any two of these $6$ points are connected by the same color, the conclusion will hold.

Otherwise, if no points among these $6$ are connected by this color, they must be connected by one of the rest two colors. In this case, this problem becomes # 2747, i.e. if $6$ points are connected using two colors, there must exist a triangle whose edges are of the same color. We know, it is true.

Hence, the original claim hold.