The answer is that there are just 2,400 different ways. 
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 different solutions.