10. (10 points) 6 football teams, each pair of teams plays at most one match. If each team plays exactly 2 matches, then the number of possible match arrangements is $\qquad$.
【Solution】Solution: 6 teams are divided into 2 groups of 3 each, and the 3 teams in each group play against each other: Grouping methods: $(6 \times 5 \times 4)$
$\div(3 \times 2 \times 1) \div 2=10$ (selecting 3 teams and the remaining 3 teams is repeated, so divide by 2);
6 teams form a circle, and adjacent teams play against each other: Method: $5 \times 4 \times 3 \times 2 \times 1 \div 2=60$ (clockwise and counterclockwise are repeated, so divide by 2),
Therefore, there are a total of $10+60=70$ valid match arrangements.
Answer: There are 70 valid match arrangements.
So the answer is: 70.