All the letters of the word MOTHER are arrang | vedclass

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(D) The letters of the word $MOTHER$ in alphabetical order are: $E, H, M, O, R, T$.Total number of letters is $6$. Total permutations = $6! = 720$.To

Vedclass · Accepted Answer

$411$

Vedclass · Answer

(D) The letters of the word $MOTHER$ in alphabetical order are: $E, H, M, O, R, T$.Total number of letters is $6$. Total permutations = $6! = 720$.To find the rank of $MOTHER$:$1$. 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$$8$. Words starting with $MOTE$: $2! = 2$$9$. Words starting with $MOTH E R$: $1$Sum of ranks = $120 + 120 + 24 + 24 + 6 + 6 + 6 + 2 + 1 = 309$.The rank of $MOTHER$ is $309$.The number of words appearing after $MOTHER$ = $720 - 309 = 411$.

All the letters of the word $MOTHER$ are arranged in all possible ways and the resulting words (may or may not have meaning) are arranged as in the dictionary. The number of words that appear after the word $MOTHER$ is

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