Simple question?

[Amid Cent]

I was trying to figure out how many possible results can be achieved by playing 2 10-person SNG's at the same time.

Intuitively, the answer should be: 10 finishes in the first tournament times 10 in the second. Then divide by 2, since order does not matter. That gives you 100/2 = 50.

However, the correct answer is actually 55. You can get this by sort of "freezing" the first finish, and counting each finish in the second. You then get 10 + 9 + 8 + ... + 1 = 55.

Is my logic in the first paragraph way off? Or did I just assume incorrectly?

Thanks.