The letters of the word $W O M A N$ are written in all possible orders and these words are written out as in a dictionary then find the rank of the word $W O M A N$ .

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Solution

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 $117.$

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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.

WOMAN -A⟶4!M⟶4!N⟶4!O⟶4! W⟶A⟶3! M⟶3! N⟶3! O⟶A⟶2! M⟶A⟶N⟶1⇒ Rank =4×4!+3×3!+2!+1 =96+18+2+1 =117Hence, the answer is 117.

The letters of the word $W O M A N$ are written in all possible orders and these words are written out as in a dictionary then find the rank of the word $W O M A N$ .

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 $117.$