Seven teams, divided into two groups, participated in the football tournament in my neighborhood. Group 1 consisted of the teams Avaqui, Botágua, and Corinense. Group 2 consisted of the teams Dinossaurs, Esquisitos, Flurinthians, and Guaraná.

$\mathrm{In}$ the first round of the tournament, each team played against each of the other teams in its group exactly once. In the second round of the tournament, each team played against each of the teams in the other group exactly once.

(a) How many matches were played in the first round in Group 1?

(b) How many matches were played in the first round in Group 2?

(c) How many matches were played in the second round?
Let's denote the seven teams by their initial letter.
(a) In the first round of Group 1, three matches were played: $\mathrm{A} \times \mathrm{B}, \mathrm{B} \times \mathrm{C}$, and $\mathrm{C} \times \mathrm{A}$.

(b) In the first round of Group 2, six matches were played: $\mathrm{D} \times \mathrm{E}, \mathrm{D} \times \mathrm{F}$, $\mathrm{D} \times \mathrm{G}, \mathrm{E} \times \mathrm{F}, \mathrm{E} \times \mathrm{G}$, and $\mathrm{F} \times \mathrm{G}$.

(c) In the second round, each team in Group 1 played four matches, one against each team in Group 2. Since Group 1 has three teams, in the second round, $3 \times 4=12$ matches were played.