(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

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(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 $MOT E$: $2! = 2$Words starting with $MOT H E R$: $1$Total rank = $120 + 120 + 24 + 24 + 6 + 6 + 6 + 2 + 1 = 309$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

If the letters of the word $MOTHER$ are permuted and all the words so formed (with or without meaning) are listed as in a dictionary,then the position of the word $MOTHER$ is

JEE MAIN 2020 All JEE MAIN

A
$307$
B
$308$
C
$310$
D
$309$

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Permutations and Combinations

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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If the letters of the word $MOTHER$ are permuted and all the words so formed (with or without meaning) are listed as in a dictionary,then the position of the word $MOTHER$ is

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