In a certain soccer league, each of the five teams plays every other team in the league exactly three times each season. How many games are played in total in one season?

a) 15
b) 24
c)30
d)60
e)120

To find out how many games are played in total in one season, we need to calculate the total number of games for each team and then sum them up for all the teams.

In a certain soccer league with five teams, each team plays every other team three times. Let's break it down:

Team 1 plays three games against the other four teams.
Team 2 plays three games against the other four teams.
Team 3 plays three games against the other four teams.
Team 4 plays three games against the other four teams.
Team 5 plays three games against the other four teams.

To find the total number of games for each team, we can use the combination formula nC2, which calculates the number of combinations possible when choosing 2 items from a set of n items.

For each team, we need to calculate the number of combinations possible when choosing 2 opponents from the remaining 4 teams. Using the nC2 formula, we get:

Team 1: 4C2 = 6 games (plays against teams 2, 3, 4, 5)
Team 2: 4C2 = 6 games (plays against teams 1, 3, 4, 5)
Team 3: 4C2 = 6 games (plays against teams 1, 2, 4, 5)
Team 4: 4C2 = 6 games (plays against teams 1, 2, 3, 5)
Team 5: 4C2 = 6 games (plays against teams 1, 2, 3, 4)

Adding up the games for each team, we get:

6 + 6 + 6 + 6 + 6 = 30 games.

Therefore, the correct answer is option c) 30.

how many combinations of five taken 2 at a time?

C(5,2) = 5!/2!(3!) = 10
so 30