Question about a method in elementary combinatorics. I'm reading Martin's: Counting: The Art of Enumerative Combinatorics.

How many ways are there to arrange the letters in NASHVILLETENNESSEE with the first N precending the first S and with the first $E$ preceding the $T$?

The author argues that we can consider first the problem of arranging only the 3 N's and the 3 S's, suppose we want to begin by putting down the 3 S's, then we have $.S.S.S.$ where the dots are the place in which the N's should be placed. And he says that the first place must be ocuppied, giving $NS.S.S.$
I don't understand why we have only one dot between the S's, if we have two remaining N's why isn't it $N..S..S..S..$?

Starting with $N..S$ would also include the cases where the $second$ and possibly the $third$ N also precedes the first S.


You have not posted the rest of the reasoning in the book after $NS.S.S.$, but it should be basically to place 2 N-s at the 3 remaining dot positions, making sure you do not repeat cases.

If choosing the first dot is denoted by 1, second dot by 2 etc, the options of putting 2 N-s are by choosing these dots: 
11
12
13
22
23
