In how many ways can the letters of the word | vedclass

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(D) The word '$EXCELLENT$' consists of $9$ letters in total.The frequency of each letter is as follows: $E$ appears $3$ times,$X$ appears $1$ time,$C$

Vedclass · Accepted Answer

$30240$

Vedclass · Answer

(D) The word '$EXCELLENT$' consists of $9$ letters in total.The frequency of each letter is as follows: $E$ appears $3$ times,$X$ appears $1$ time,$C$ appears $1$ time,$L$ appears $2$ times,$N$ appears $1$ time,and $T$ appears $1$ time.The total number of arrangements is given by the formula $\frac{n!}{p!q!...}$,where $n$ is the total number of letters and $p, q, ...$ are the frequencies of repeating letters.Here,$n = 9$,$p = 3$ (for $E$),and $q = 2$ (for $L$).$	ext{Required arrangements} = \frac{9!}{3! 	imes 2!} = \frac{362880}{6 	imes 2} = \frac{362880}{12} = 30240$.

In how many ways can the letters of the word '$EXCELLENT$' be arranged?

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