If the letters of the word EAMCET are permuted in all possible ways and if the words thus formed are arranged in the dictionary order, find the rank of the word EAMCET.

Explanation

The dictionary order of the letters of the word EAMCET is
A C E E M T
In the dictionary order first gives the words which begin with the letter A.
If we fill the first place with A, remaining 5 letters can be arranged in `(5!)/(2!)` ways (since there are 2 E's) on proceeding like this, we get
`A rarr (5!)/(2!)` words
`C rarr (5!)/(2!)` words
`EAC rarr 3!` words
`EAE rarr 3!` words
`EAMCET rarr 1` word
Hence the rank of the word EAMCET is
`=2xx(5!)/(2!)+2xx3!+1`
`=120+12+1=133`