Hi Tina, this question is a pretty interesting one.

To start, we need to figure out how many teams there are. Since each team won 10 and lost 10 games, there must be 21 teams in total.

Hence, there are $\binom{21}{3} = 1330$ sets of three teams in total.

We want to count how many of these sets have each team beating another team in the group of 3.

Here's a hint for how to proceed. Note that in ANY of these sets of 3 teams, either (i) one team beats the other two teams (what we don't want) or (ii) each team beats another team (what we want) and no other outcome is possible. These are roughly shown in the picture below (where an arrow denotes a team beating another):

Therefore, if you can count the number of outcomes in possibility (i) on the left, then you can subtract that number from the total. Be a little careful, remember the set of three is chosen in no particular order.

Give this a try and let us know if you have additional questions. The fact that each team won 10 games will probably be needed again here.