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There are 13 distinct seats lined up in a row in a room. There are 13...

There are 13 distinct seats lined up in a row in a room. There are 13 of each kind of person in the room: hobbits, humans, and giants. Hobbits take up one seat each. Humans take up two each and giants each need 4 seats. If all hobbits are identical; all humans are identical; and all giants are identical, then how many different ways are there for some of the people to sit in the 13 seats?

I know the answer is 816, but I don't know how to work this out.

math   Statistics-And-Probability   
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