If the letters of the word ‘MOTHER’ are written in all possible orders and these words are written out as in a dictionary, find rank of the word ‘MOTHER’.

Explanation

In the dictionary the words at each stage are arranged in alphabetical order.

In the given problem we must therefore consider the words beginning with `E, H, M, 0, R, T`

∴ Number of words starting with `E = 5! `

`= 5×4×3×2×1=120`

Number of words starting with `H 5!`

`=120`

Number of words beginning with `M` is `5!,`

Number of words starting with `ME = 4! = 4×3×2×1 = 24 `

...