Find the number of permutation of all the letters of the word MATHEMATICS which starts with consonants only.

Explanation

We have letters (M M), (A A), (T T),H,E,I,C,S
Number of words starting with M to T `=(10!)/(2!xx2!)`
`(because` Two pairs of identical letters are available)
Number of words starting with T or C or S=`(10!)/(2!xx2!xx2!)`
`(because` Three pairs of identical letters are available)
Therefore, total number of words `=2xx(10!)/(2!xx2!)+3xx(10!)/(2!xx2!xx2!)`
`=(7xx10!)/(2!xx2!xx2!)`