in the letters of rachit are arranged in all possible ways and these words are written out as in a dictionary what is rank of rachit

RACHIT consist of 6 different letters A,C,H,I,R,T.
Dictionary arranges words alphabetically. This means all the words starting with A,C,H,I comes before RACHIT in the dictionary.
Total number of words starting with A- A_ _ _ _ _ = 5!
Similarly number of words starting with C,H and I are also 5!
First word starting with R is the word that has all other letters except R arranged alphabetically. Luckily, in RACHIT every other letter is arranged alphabetically. This means RACHIT is the first word in the dictionary starting with R. Numbers before RACHIT are 5!X4=480.
So, rank of RACHIT is 481.