Find the no. of Permutations of all the letters of the word MATHEMATICS which starts with consonants only

(MM), (AA), (TT), H, E, I, C, S

Words starting with M or T $=\frac{2\times 10!}{2!2!}$

Words starting with H, C, S  $=\frac{3\times 10!}{2!2!2!}$

Hence number of words are

$\begin{array}{l}\frac{2\times 10!}{2!2!}+\frac{3\times 10!}{2!2!2!}\\ =\frac{10!}{2}+\frac{3\times 10!}{8}\\ =\frac{4\times 10!+3\times 10!}{8}\\ =\frac{7\times 10!}{8}\end{array}$