Find the number of words which can be formed using all the letters of the word 'INSTITUTION' which start with consonant.

Answer

`(10!)/(3!3!)+(10!)/(3!3!2!)+(10!)/(3!2!2!)`

Explanation

We have letters (I, I, I), U, O, (N,N),S,(T,T,T)
Words start with consonant.
Case I: Words start with N
We have to arrange (I,I,I)U,O,N,S,(T,T,T)
Number of words are `(10!)/(3!3!)`
Case II : Words start with S
We have to arrange (I,I,I),U,O,(N,N),(T,T,T)
Number of words are `(10!)/(3!3!2!)`
Case III : Words start with T
We have to arrange (I,I,I),U,O,(N,N),S,(T,T)
Number of words are `(10!)/(3!2!2!)`
So, total number of words are `(10!)/(3!3!)+(10!)/(3!3!2!)+(10!)/(3!2!2!)`.