If all the seven letters of the word LEADING | vedclass

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(B) First,we arrange the letters of the word $LEADING$ in alphabetical order: $A, D, E, G, I, L, N$. Words starting with $A$: $6! = 720$. Words starti

Vedclass · Accepted Answer

$ELNADGI$

Vedclass · Answer

(B) First,we arrange the letters of the word $LEADING$ in alphabetical order: $A, D, E, G, I, L, N$. Words starting with $A$: $6! = 720$. Words starting with $D$: $6! = 720$. Words starting with $E$: $6! = 720$. Total words starting with $A, D, E$ is $720 + 720 + 720 = 2160 > 2017$. So,the word starts with $E$. Words before $E$ are $720 + 720 = 1440$. Now,words starting with $EA, ED, EG, EI$: $4 	imes 5! = 4 	imes 120 = 480$. Total words up to $EI$: $1440 + 480 = 1920$. Next,words starting with $ELA, ELD, ELG$: $3 	imes 4! = 3 	imes 24 = 72$. Total words up to $ELG$: $1920 + 72 = 1992$. Next,words starting with $ELI$: $4! = 24$. Total words up to $ELI$: $1992 + 24 = 2016$. The $2017^{	ext{th}}$ word must be the first word starting with $ELN$. The remaining letters after $ELN$ are $A, D, G, I$ in alphabetical order. Thus,the $2017^{	ext{th}}$ word is $ELNADGI$.

If all the seven letters of the word $LEADING$ are permuted in all possible ways and the words thus formed are arranged as in the dictionary order,then the word in $2017^{\text{th}}$ place is

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