Question:
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of
the word 'MOTHER' is
Solution:
MOTHER
$1 \rightarrow \mathrm{E}$
$2 \rightarrow \mathrm{H}$
$3 \rightarrow \mathrm{M}$
$4 \rightarrow \mathrm{O}$
$5 \rightarrow \mathrm{R}$
$6 \rightarrow \mathrm{T}$
So position of word MOTHER in dictionary
$2 \times 5 !+2 \times 4 !+3 \times 3 !+2 !+1$
$=240+48+18+2+1$
$=309$