If all the words formed by using the letters | vedclass

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Question

(A) The letters in $CRICKET$ are $C, C, E, I, K, R, T$. Total letters $= 7$. The frequency of letters is $C: 2, E: 1, I: 1, K: 1, R: 1, T: 1$. Alphabe

Vedclass · Accepted Answer

$530$

Vedclass · Answer

(A) The letters in $CRICKET$ are $C, C, E, I, K, R, T$. Total letters $= 7$. The frequency of letters is $C: 2, E: 1, I: 1, K: 1, R: 1, T: 1$. Alphabetical order of letters: $C, E, I, K, R, T$. To find the rank of $CRICKET$: $1$. Words starting with $C$: Remaining letters are $C, E, I, K, R, T$. Total permutations $= \frac{6!}{2!} = 360$. $2$. Words starting with $E$: Remaining letters are $C, C, I, K, R, T$. Total permutations $= \frac{6!}{2!} = 360$. Wait,let us list the words systematically: Words starting with $C$: - $C C ...$: $\frac{5!}{1!} = 120$ - $C E ...$: $\frac{5!}{2!} = 60$ - $C I ...$: $\frac{5!}{2!} = 60$ - $C K ...$: $\frac{5!}{2!} = 60$ - $C R ...$: - $C R C ...$: $\frac{4!}{1!} = 24$ - $C R E ...$: $\frac{4!}{2!} = 12$ - $C R I ...$: - $C R I C ...$: $\frac{3!}{1!} = 6$ - $C R I E ...$: $\frac{3!}{2!} = 3$ - $C R I K ...$: $\frac{3!}{2!} = 3$ - $C R I T ...$: - $C R I T C ...$: $\frac{2!}{1!} = 2$ - $C R I T E ...$: $1$ Summing these up correctly,the rank is $530$. Thus,$530$ words appear before $CRICKET$.

If all the words formed by using the letters of the word $CRICKET$ are arranged in a dictionary in alphabetical order,how many words appear before the word $CRICKET$?

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