The letters of the word MODESTY are written i | vedclass

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Question

(C) The word $MODESTY$ consists of $7$ distinct letters: $D, E, M, O, S, T, Y$.To find the rank,we arrange the letters in alphabetical order: $D, E, M

Vedclass · Accepted Answer

$1681$

Vedclass · Answer

(C) The word $MODESTY$ consists of $7$ distinct letters: $D, E, M, O, S, T, Y$.To find the rank,we arrange the letters in alphabetical order: $D, E, M, O, S, T, Y$.$1$. Words starting with $D$: $6! = 720$ words.$2$. Words starting with $E$: $6! = 720$ words.$3$. Words starting with $MD$: $5! = 120$ words.$4$. Words starting with $ME$: $5! = 120$ words.$5$. The next word starts with $MO$. The letters remaining are $D, E, S, T, Y$. Arranging these alphabetically gives $D, E, S, T, Y$. Thus,the first word starting with $MO$ is $MODESTY$.Rank $= 720 + 720 + 120 + 120 + 1 = 1681$.

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

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