Duct-tape two green bottles together.In how many different ways can I arrange 7 green and 8 brown bottles
so that exactly one pair of green bottles are side by side?
Now we have 14 units to arrange:
Now place the eight brown bottles in a row.
. . Note that there are spaces before, after and between them.
. . .
We will take the six green units and place them in six of the nine spaces.
And there are: . ways.