Question

If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the work Mother.

Answer 1

Order is E, H, M, O, R, T

words with E _ _ _ _ _$=5!=120$

words with H _ _ _ _ _$=5!=120$

words with ME _ _ _ _$=4!=24$

words with MH _ _ _ _$=4!=24$

words with MOE _ _ _$=3!=6$

words with MOH _ _ _$=3!=6$

words with MOR _ _ _$=3!=6$

words with MOTE_ _$=2!=2$

___________

words with MOTHER$=308$

$\Rightarrow {309}^{th}$ word.