How many different ways can we place 4 identical rooks on the following chess board How many different ways can we place 4 identical rooks on the following chess board so that no two of them attack each other?

I know when the board is $n \times n$ and we have $n$ towers then the solution is simply $n!$
However I am not sure how to solve the problem in this case.

Just to verify that Bram28's answer is correct, we can count it up by building the graph whose 32 vertices are the positions on the board, with edges for rook attacks. Then count the number of independent sets of size four.
Here's Sage code to do that:
from sage.graphs.independent_sets import IndependentSets

posns = [(x,y) for x in range(7) for y in range(max(3-x,x-3),min(5+x,11-x))]
def isedge(a,b):
    return (a[0]==b[0]) != (a[1]==b[1])
G = Graph([posns, isedge])
print(sum(len(x) == 4 for x in IndependentSets(G)))

And here it is on SageCell.  The answer 3532 agrees with Bram28's enumeration.
