A small class of nine boys are to change their seating arrangement by drawing their new seat numbers from a box. After the seat change, what is the probability that there is only one pair of boys who have switched seats with each other and only three boys who have unchanged seats?
How do you solve this? I've thought of $\frac{(9C2)(7C3)(4!)}{9!}$ to give the answer, but then I realize the $4!$ includes arrangements for the 4 boys switching seats with each other and having unchanged seats. How do I account for these conditions in this problem?