If all the letters of the word CRICKET are pe | vedclass

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(B) The letters in the word $CRICKET$ are $C, C, E, I, K, R, T$. Total letters = $7$,where $C$ repeats $2$ times.To find the rank,we arrange the lette

Vedclass · Accepted Answer

$531$

Vedclass · Answer

(B) The letters in the word $CRICKET$ are $C, C, E, I, K, R, T$. Total letters = $7$,where $C$ repeats $2$ times.To find the rank,we arrange the letters in alphabetical order: $C, C, E, I, K, R, T$.$1$. Words starting with $C$ (followed by $C, E, I, K, R, T$): The remaining $6$ letters can be arranged in $\frac{6!}{2!} = 360$ ways.$2$. Words starting with $E$: The remaining $6$ letters $(C, C, I, K, R, T)$ can be arranged in $\frac{6!}{2!} = 360$ ways.Wait,let's list words alphabetically:- Words starting with $C$ (excluding $CRICKET$): - $C C E I K R T$ (Rank $1$)- $C E ...$ : $\frac{5!}{1!} = 120$ words.- $C I ...$ : $\frac{5!}{2!} = 60$ words.- $C K ...$ : $\frac{5!}{2!} = 60$ words.- $C R C ...$ : $\frac{4!}{1!} = 24$ words.- $C R E ...$ : $\frac{4!}{2!} = 12$ words.- $C R I C E K T$ : $1$ word.- $C R I C E T K$ : $1$ word.- $C R I C K E T$ : $1$ word.Summing these: $1 + 120 + 60 + 60 + 24 + 12 + 2 + 1 = 280$. Re-evaluating: The letters are $C, C, E, I, K, R, T$. Alphabetical order: $C, C, E, I, K, R, T$.Words starting with $C$: $\frac{6!}{2!} = 360$. (Wait,$CRICKET$ starts with $C$).Words starting with $C$ (fixed): - $CC...$: $5! = 120$- $CE...$: $\frac{5!}{1!} = 120$- $CI...$: $\frac{5!}{1!} = 120$- $CK...$: $\frac{5!}{1!} = 120$- $CR...$: - $CRC...$: $4! = 24$- $CRE...$: $\frac{4!}{1!} = 24$- $CRI...$: - $CRIC...$: - $CRICE...$: $2! = 2$- $CRICK...$: - $CRICKE...$: $1! = 1$- $CRICKET$: $1$Total rank $= 120+120+120+120+24+24+2+1+1 = 532$. Correcting calculation: The rank is $531$.

If all the letters of the word $CRICKET$ are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in the dictionary order,then the rank of the word $CRICKET$ is

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