If the letters of the word SACHIN are arrange | vedclass

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(D) The letters of the word $SACHIN$ are $A, C, H, I, N, S$ in alphabetical order.To find the rank of $SACHIN$,we count the number of words starting w

Vedclass · Accepted Answer

$601$

Vedclass · Answer

(D) The letters of the word $SACHIN$ are $A, C, H, I, N, S$ in alphabetical order.To find the rank of $SACHIN$,we count the number of words starting with letters before $S$ in the alphabetical list.The letters before $S$ are $A, C, H, I, N$.Each of these letters,when placed in the first position,allows the remaining $5$ letters to be arranged in $5!$ ways.Number of words starting with $A, C, H, I, N = 5 	imes 5! = 5 	imes 120 = 600$.The next word in the dictionary order is $SACHIN$ itself.Therefore,the rank of $SACHIN$ is $600 + 1 = 601$.

If the letters of the word $SACHIN$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $SACHIN$?

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