The number of arrangements of the letters of | vedclass

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(C) The word $SALOON$ contains $6$ letters: $S, A, L, O, O, N$,where $O$ repeats $2$ times.Total number of arrangements = $\frac{6!}{2!} = \frac{720}{

Vedclass · Accepted Answer

$240$

Vedclass · Answer

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

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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