a counting problem (songs)

Mar 2010
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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
 

Soroban

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May 2006
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Hello, ihavvaquestion!

Your mobile music DJ business has: 6 rap, 10 rock, 6 alternative,
8 oldies and 5 C&W 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:

. . \(\displaystyle (_6C_2)(_{10}C_2)(_6C_2)(_8C_2)(_5C_2) \;=\; 2,\!835,\!000\) choices.
This is correct if the order of the 10 songs in not important.

If the order of the songs is considered, mutilply by 10-factorial.

 
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