What is the rank of the word "MOTHER" when all possible words are formed using all its letters and arranged…
What is the rank of the word "MOTHER" when all possible words are formed using all its letters and arranged as in a dictionary?
$308$
$309$
$291$
$307$
Solution
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 $=308+1=309$