Nine students enter a classroom with 15 desks. How many seating arrangements are possible if each student selects a desk?
p = n!/(n-r)! = 165110400 doesn't sound right
I have no idea how you got that answer. BUT
$\displaystyle P(15,9)=\dfrac{15!}{6!}=1816214400$
In any normal classroom the seats are different: perhaps numbered.
The students are clearly distinct.
So this is a permutation of 15 taken 9 at a time.