If all the seven letters of the word LEADING | vedclass

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Question

(B) The letters of the word $LEADING$ in alphabetical order are $A, D, E, G, I, L, N$.Total number of letters is $7$. The total number of permutations

Vedclass · Accepted Answer

$ELNADGI$

Vedclass · Answer

(B) The letters of the word $LEADING$ in alphabetical order are $A, D, E, G, I, L, N$.Total number of letters is $7$. The total number of permutations is $7! = 5040$.Words starting with $A$: $6! = 720$.Words starting with $D$: $6! = 720$.Total words starting with $A$ or $D$ is $720 + 720 = 1440$.Words starting with $E$:$EA... = 5! = 120$$ED... = 5! = 120$$EG... = 5! = 120$$EI... = 5! = 120$Total words starting with $A, D$ or $EA, ED, EG, EI$ is $1440 + 480 = 1920$.Next,words starting with $EL$:$ELA... = 4! = 24$$ELD... = 4! = 24$$ELG... = 4! = 24$$ELI... = 4! = 24$Total words up to $ELI...$ is $1920 + 96 = 2016$.The $2017^{	ext{th}}$ word must start with $ELN...$. The remaining letters 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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