A relay for the whole class

A class of thirty children organised its own relay tournament. The teacher split the class into five teams of six.

$30$ children, $5$ teams of $6$: $30÷6=5$.

$30÷6=5$ teams.

Each team raced against every other team exactly once. That made ten races.

Each team against each other team once: $\frac{5\times 4}{2}=10$ races.

Races: $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$.

Each race took four minutes, so all the races together took forty minutes. The lesson lasts forty-five, so five minutes were left for the prize-giving.

$10\times 4=40$ min of racing; the lesson is $45$ min, so $45-40=5$ min for prizes.

$10\times 4=40$, and $45-40=5$.

The teams finished with four, three, two, one and no wins: all different. Together that is exactly ten, because every race has just one winner.

Wins: $4,3,2,1,0$, and $4+3+2+1+0=10$, since each race has one winner.

Wins: $4+3+2+1+0=10=\left(\genfrac{}{}{0ex}{}{5}{2}\right)$.