From any letter in the diagram, a move can only be made to a letter diagonally adjacent and below. In how many different ways can a path that spells MATHCOUNTS be taken?
\(\begin{array}{ccccccccc} & & & &M& & & & \\ & & &A& &A& & & \\ & &T& &T& &T& & \\ &H& &H& &H& &H& \\ C& &C& &C& &C& &C\\ &O& &O& &O& &O& \\ & &U& &U& &U& & \\ & & &N& &N& & & \\ & & & &T& & & & \\ & & & & &S& & & \\ \end{array}\)
