What is the rank of the word "MOTHER" when all possible words are formed using all its letters and arranged as in a dictionary?

Total words $=6 \mathrm{i}=720$ Number of words before starting with 'M' $=2 \times 5 i=2 \times 120=240$ Number of words starts with $\mathrm{M}$ and second letterbeore ${ }^{\prime} \mathrm{o}^{\prime}=2 \mathrm{x} 4 \mathrm{i}=48$ Number of words with first two letters are MOand third letter before $\mathrm{T}=3 \times 3 \mathrm{i}=18$ Number of words with first three letter are MOT and fourth letter before $\mathrm{H}=2 \mathrm{i}=2$ Total words till now $=240+48+18+2=308$ $\therefore$ Next words $=$ MOTHER So, Rank of MOTHER $=308+1=309$