<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Jia and Yi are playing a table tennis match in a best of three series. In each game, the first player to reach 11 points while the other has less than 10 points wins; if the score is tied at 10, the first player to win by 2 points wins. The total score between Jia and Yi in the three games is 30 points. How many possible score scenarios are there for the three games without considering the order of the scores? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
8
Jia and Yi are playing a table tennis match in a best of three series. In each game, the first player to reach 11 points while the other has less than 10 points wins; if the score is tied at 10, the first player to win by 2 points wins. The total score between Jia and Yi in the three games is 30 points. How many possible score scenarios are there for the three games without considering the order of the scores?
test