In how many different ways can the letters of | vedclass

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(A) The word '$OFFICES$' contains $7$ letters in total.In this word,the letter '$F$' is repeated $2$ times,while all other letters $(O, I, C, E, S)$ a

Vedclass · Accepted Answer

$2520$

Vedclass · Answer

(A) The word '$OFFICES$' contains $7$ letters in total.In this word,the letter '$F$' is repeated $2$ times,while all other letters $(O, I, C, E, S)$ appear once.The number of ways to arrange $n$ objects where $p$ objects are of one kind and $q$ objects are of another kind is given by the formula $\frac{n!}{p!q!...}$.Here,$n = 7$ and $p = 2$ (for the letter '$F$').Therefore,the required number of arrangements $= \frac{7!}{2!} = \frac{5040}{2} = 2520$.

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

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