If the letters of the word MOTHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MOTHER is

Question

Infinity Learn · Accepted Answer

E H M O R T $$(alphabetical$$ $$order)Number$$ of words beginning withE $$_$$ $$_$$ $$_$$ $$_$$ $$_$$ $$=$$ $$5$$!H $$_$$ $$_$$ $$_$$ $$_$$ $$_$$ $$=$$ $$5$$!M E $$_$$ $$_$$ $$_$$ $$_$$ $$=$$ $$4$$!M H $$_$$ $$_$$ $$_$$ $$_$$ $$=$$ $$4$$!M O E $$_$$ $$_$$ $$_$$ $$=$$ $$3$$!M O H $$_$$ $$_$$ $$_$$ $$=$$ $$3$$!M O R $$_$$ $$_$$ $$_$$ $$=$$ $$3$$!M O T E $$_$$ $$_$$ $$=$$ $$2$$!M O T H E R $$=$$ $$1$$!$$__________________$$∴ Rank of word MOTHER $$=$$ $$309$$

If the letters of the word MOTHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MOTHER is

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