Question

The letters of the word $WOMAN$ are written in all possible orders and these words are written out as in a dictionary then find the rank of the word $WOMAN$.

Answer 1

WOMAN -

$A⟶4!$

$M⟶4!$

$N⟶4!$

$O⟶4!$

$W⟶A⟶3!$

$M⟶3!$

$N⟶3!$

$O⟶A⟶2!$

$M⟶A⟶N⟶1$

$\Rightarrow$ Rank $=4\times 4!+3\times 3!+2!+1$

$=96+18+2+1$

$=117$

Hence, the answer is $117.$