If the letters of the word "CAPITAL" are perm | vedclass

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Question

(A) The word is $CAPITAL$. The letters in alphabetical order are $A, A, C, I, L, P, T$. Total letters = $7$. The letter $A$ repeats $2$ times. Words s

Vedclass · Accepted Answer

$802$

Vedclass · Answer

(A) The word is $CAPITAL$. The letters in alphabetical order are $A, A, C, I, L, P, T$. Total letters = $7$. The letter $A$ repeats $2$ times. Words starting with $A$: The remaining letters are $A, C, I, L, P, T$ ($6$ letters). Number of arrangements = $\frac{6!}{1!} = 720$. Words starting with $C$: Next letter is $A$: Remaining letters are $A, I, L, P, T$ ($5$ letters). Number of arrangements = $5! = 120$. Next letter is $C$ (not possible). Next letter is $I$: Remaining letters are $A, A, L, P, T$ ($5$ letters). Number of arrangements = $\frac{5!}{2!} = 60$. Next letter is $L$: Remaining letters are $A, A, I, P, T$ ($5$ letters). Number of arrangements = $\frac{5!}{2!} = 60$. Next letter is $P$: Remaining letters are $A, A, I, L, T$ ($5$ letters). Number of arrangements = $\frac{5!}{2!} = 60$. Next letter is $T$: Remaining letters are $A, A, I, L, P$ ($5$ letters). Number of arrangements = $\frac{5!}{2!} = 60$. Wait,let us re-evaluate: Alphabetical order: $A, A, C, I, L, P, T$. Words starting with $A$: $\frac{6!}{1!} = 720$. Words starting with $C$: $CA...$: Remaining letters $A, I, L, P, T$. $CAA...$: $4! = 24$. $CAI...$: $4! = 24$. $CAL...$: $4! = 24$. $CAP...$: $CAPA...$: $3! = 6$. $CAPI...$: $CAPIA...$: $2! = 2$. $CAPIL...$: $CAPILA...$: $1! = 1$. $CAPITAL$: $1$. Total rank = $720 + 24 + 24 + 24 + 6 + 2 + 1 + 1 = 802$.

If the letters of the word "$CAPITAL$" are permuted in all possible ways and the words are arranged in a dictionary order,then the rank of the word "$CAPITAL$" is

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