If the letters of the word MOTHER are arrange | vedclass

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Question

(D) The letters of the word $MOTHER$ are $E, H, M, O, R, T$ in alphabetical order.Words starting with $E$: $5! = 120$Words starting with $H$: $5! = 12

Vedclass · Accepted Answer

$309$

Vedclass · Answer

(D) The letters of the word $MOTHER$ are $E, H, M, O, R, T$ in alphabetical order.Words starting with $E$: $5! = 120$Words starting with $H$: $5! = 120$Words starting with $ME$: $4! = 24$Words starting with $MH$: $4! = 24$Words starting with $MOE$: $3! = 6$Words starting with $MOH$: $3! = 6$Words starting with $MOR$: $3! = 6$Words starting with $MOT E H R$: $1! = 1$Words starting with $MOT H E R$: $1! = 1$Summing these up: $120 + 120 + 24 + 24 + 6 + 6 + 6 + 1 + 1 = 308$.The next word is $MOTHER$,so the rank is $308 + 1 = 309$.

If the letters of the word $MOTHER$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $MOTHER$?

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