In how many ways can the letters of the word SOCKS be arranged in a line so that the two S's are together? In how many arrangements can the letters in SLOOPS be arranged so that the two O's are together?
I would think the answer to the first one would be: Treat the two S's as one entity and permute the letters: 4! and divide by 2! to account for the identical element S.Apparently not. However for the second question, you are able to use this method?
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$\begingroup$For the first question, you are arranging $\fbox{SS}\text{OCK}$, where $\fbox{SS}$ is a single entity, so there are $4$ different elements and the permutations work out to $4!$ without further adjustment.
For the second question, you are arranging $\fbox{OO}\text{SLPS}$, where again $\fbox{OO}$ is a single entity, so there are $5$ elements of $4$ different values, one of which is repeated, and the permutations work out to $5!/2! = 60$, the division by $2!$ adjusting for the repeated S.
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