Question

The number of baseball games that must be scheduled in a league with n teams is given by where each team plays every other team exactly once. A league schedules 15 games. How many teams are in the league?

Answer 1

To find the number of teams in a league that schedules 15 games where each team plays every other team once, you can use the combination formula n(n - 1)/2 = 15, which results in 6 teams.

Step-by-step explanation:

To determine the number of teams in a league that schedules 15 games, where each team plays every other team exactly once, one can use the formula for the number of combinations of n teams taken 2 at a time (since each game involves 2 teams), which is given by the formula n(n - 1)/2. Therefore, we need to find a number n such that n(n - 1)/2 = 15.

1. Let's write down the equation based on the formula: n(n - 1)/2 = 15.
2. Multiply both sides of the equation by 2 to get rid of the denominator: n(n - 1) = 30.
3. Now we need to find two consecutive integers that multiply to 30. By inspection or trial and error, we find that when n = 6, we have 6(6 - 1) = 30.
4. Therefore, the league must have 6 teams.