Find the number of permutations of $n$ different things taken $r$ at a time so that two particular things are always included and are together?
Including two things initially, i have $(n-2)$ things from which I can choose $(r-2)$ things. Hence $\,^{(n-2)}C_{(r-2)}$ denote the combinations which can be arranged in $(r-2)!$
The two things can be interchanged in 2! ways within themselves.
Furthermore, when $r$ things are selected, I have $r+1$ ways where I can insert two things which have to remain together.
So I get $\,^{(n-2)}C_{(r-2)} \cdot (r-2)! \cdot 2! \cdot (r+1)$
Am I doing the right thing?