Your mobile music dj business has 6 rap, 10 rock, 6 alternative, 8 oldies and 5 country cd singles. How many different 10-song sets can the dj play at a party if she plays exactly two singles from each?

Here is how I came up with an answer:

6C2 * 10C2 * 6C2 * 8C2 * 5C2 = 2,835,000 choices

I think this is correct, but was hoping for confirmation