Basically we need to know how many solutions there are in the non-negative integers to the equation p+n+d+q=11, where the letters represent the numbers of coin types.

By common practice we regard the coins of any one type to be identical.

The answer is C(11+4-3,11).

In this case, the only ways we found above that cannot be used are the 4 cases where all 11 coins are of the same type. So subtract.