The number of arrangements of the letters of | vedclass

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(C) The word $SALOON$ contains $6$ letters,where $O$ repeats $2$ times.Total number of arrangements of the letters of the word $SALOON$ is given by $\

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(C) The word $SALOON$ contains $6$ letters,where $O$ repeats $2$ times.Total number of arrangements of the letters of the word $SALOON$ is given by $\frac{6!}{2!} = \frac{720}{2} = 360$.To find the number of arrangements where the two $O$'s come together,we treat the two $O$'s as a single unit $(OO)$. Now,we have $5$ units: $S, A, L, N, (OO)$.The number of arrangements of these $5$ units is $5! = 120$.Therefore,the number of arrangements where the two $O$'s do not come together is the total arrangements minus the arrangements where they are together:$360 - 120 = 240$.

The number of arrangements of the letters of the word $SALOON$,if the two $O$'s do not come together,is

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