what is the rank of word MOTHER when the letter of the word are arranged alphabetically as in a dictionary is.......

Arrange all the alphabets in alphabetical order like(E, H, M, O, R, T)Now in dictionary words will appear in alphabetical order, so first words will appear starting alphabet “E“. When E is fixed at first position, rest 5 alphabets can be arranged in 5! = 120 ways.Next starting alphabet will be “H” and again there will be 5! = 120 words starting with “H“.Now starting with “M“, and next alphabet as “E” we will have 4!=24 words.Similarly starting with “M“, and next alphabet as “H” we will have 4!=24 words.Next will be starting with “M“, and next alphabet as “O” and next as “E” we’ll have 3!=6 words.Similarly starting with “M“, and next alphabet as “O” and next as (“H”or“R”) we’ll have 3!*2=12 words.Next will be starting with “M“, and next alphabet as “O” and next as “T” and next as “E” we’ll have 2!=4 words. Next will be starting with “M“, and next alphabet as “O” and next as “T” and next as “H” will have 2! = 4 words but the first word will beM>O>T>H>E>Rwhich is the desired word.So the rank of wordMOTHERin dictionary will be5! + 5! + 4! +4! + 3! + 3! + 3! + 2! +1which equals309.