The answer is that
there are just 2,400
Any three coins may be taken from one side to combine with one coin
taken from the other side.
We may select three from the top in ten ways and one from
the bottom in five ways, making fifty.
But we may also select three
from the bottom and one from the top in fifty ways.
We may thus select
the four coins in one hundred ways, and the four removed may be
arranged by permutation in twenty-four ways.
Thus there are
24 × 100 = 2,400