What is the rank of the word "MOTHER" when al | vedclass

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Question

(B) The letters in the word "$MOTHER$" are $M, O, T, H, E, R$. All letters are distinct. Total number of arrangements $= 6! = 720$. Alphabetical order

Vedclass · Accepted Answer

$309$

Vedclass · Answer

(B) The letters in the word "$MOTHER$" are $M, O, T, H, E, R$. All letters are distinct. Total number of arrangements $= 6! = 720$. Alphabetical order of letters: $E, H, M, O, R, T$. $1$. Words starting with $E$: $5! = 120$. $2$. Words starting with $H$: $5! = 120$. $3$. Words starting with $ME$: $4! = 24$. $4$. Words starting with $MH$: $4! = 24$. $5$. Words starting with $MOE$: $3! = 6$. $6$. Words starting with $MOH$: $3! = 6$. $7$. Words starting with $MOR$: $3! = 6$. $8$. Words starting with $MOT E H R$: $1! = 1$. $9$. Words starting with $MOT E R H$: $1! = 1$. $10$. Words starting with $MOT H E R$: $1$. Summing these up: $120 + 120 + 24 + 24 + 6 + 6 + 6 + 1 + 1 + 1 = 309$. Therefore,the rank of the word "$MOTHER$" is $309$.

What is the rank of the word "$MOTHER$" when all possible words are formed using all its letters and arranged as in a dictionary?

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