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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.
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