I tried to do do this using inclusion-exclusion principle, and got something like this:
$ \frac{11!}{2!2!2!2!} -\binom{4}{1} \frac{10!}{2!2!2!}+\binom{4}{2} \frac{9!}{2!2!}-\binom{4}{3} \frac{8!}{2!} + \binom{4}{4}7!$
But I have no idea if it's correct. Can someone tell me if it's correct, and if it's not, why is it incorrect?