1. **State the problem:** There are 10 football teams in a league, and each team plays every other team 4 times. We need to find the total number of games played. 2. **Formula used:** The total number of games when each team plays every other team once is given by the combination formula $$\binom{n}{2} = \frac{n(n-1)}{2}$$ where $n$ is the number of teams. 3. Since each pair of teams plays 4 times, multiply the number of unique pairs by 4: $$\text{Total games} = 4 \times \frac{n(n-1)}{2}$$ 4. **Calculate:** Substitute $n=10$: $$\text{Total games} = 4 \times \frac{10 \times 9}{2}$$ 5. Simplify inside the fraction: $$\frac{10 \times 9}{2} = \frac{90}{2} = 45$$ 6. Multiply by 4: $$4 \times 45 = 180$$ 7. **Final answer:** The total number of games played is **180**.