Question 3
Six teams will take part in a volleyball tournament. Each pair of the teams should play one match. All the matches will be realized in five rounds, each involving three simultaneous matches on the courts numbered 1, 2 and 3. Find the number of all possible draws for such a tournament. By a draw we mean a table $5 \times 3$ in which an unordered pair of teams is written on the field $(i, j)$, where $i \in \{1, 2, 3, 4, 5\}$ and $j \in \{1, 2, 3\}$, if these two teams will meet each other in the $i$-th round on the court $j$. You are allowed to write down the resulting number as a product of prime factors (instead of writing its decimal expansion).