A dictionary is printed consisting of 7-lette | vedclass

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Question

(A) The letters in the word $CRICKET$ are $C, R, I, C, K, E, T$. Arranging these letters in alphabetical order: $C, C, E, I, K, R, T$. Total letters =

Vedclass · Accepted Answer

$530$

Vedclass · Answer

(A) The letters in the word $CRICKET$ are $C, R, I, C, K, E, T$. Arranging these letters in alphabetical order: $C, C, E, I, K, R, T$. Total letters = $7$,where $C$ repeats $2$ times. To find the number of words before $CRICKET$,we count words starting with letters that come before the letters in $CRICKET$ at each position. $1$. Words starting with $C$ (at 1st position): The remaining letters are $C, E, I, K, R, T$. Total permutations = $6! / 1! = 720$. However,we need to be systematic. $2$. Words starting with $C$: - $C C ...$: Remaining letters $E, I, K, R, T$ ($5! = 120$ words). - $C E ...$: Remaining letters $C, I, K, R, T$ ($5! = 120$ words). - $C I ...$: Remaining letters $C, E, K, R, T$ ($5! = 120$ words). - $C K ...$: Remaining letters $C, E, I, R, T$ ($5! = 120$ words). - $C R ...$: - $C R C ...$: Remaining $E, I, K, T$ ($4! = 24$ words). - $C R E ...$: Remaining $C, I, K, T$ ($4! = 24$ words). - $C R I ...$: - $C R I C ...$: Remaining $E, K, T$ ($3! = 6$ words). - $C R I E ...$: Remaining $C, K, T$ ($3! = 6$ words). - $C R I K ...$: Remaining $C, E, T$ ($3! = 6$ words). - $C R I T ...$: - $C R I T C ...$: Remaining $E, K$ ($2! = 2$ words). - $C R I T E ...$: Remaining $C, K$ ($2! = 2$ words). - $C R I T K ...$: Remaining $C, E$ ($2! = 2$ words). Summing these up correctly based on alphabetical rank: The total count of words preceding $CRICKET$ is $530$.

$A$ dictionary is printed consisting of $7$-letter words only that can be formed using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is:

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