Question

How many volleyball games would Rana

have had to schedule if there were 10 teams
in the league and each team played each
other twice?

Answer 1

90 games

Explanation:

Given: Total number of team (n) = 10

Each team will play twice with each other.

We know that every team will play two game with each other except with itself, therefore each team will play
`(n-1)* 2`

⇒ Each team will play =
`(10-1)* 2 = 18\ games`

∴ Each team will have 18 games with each other in the league.

Now, as there are total 10 teams and each team have 18 games each, however, we have to make sure that no team have more than two games with other team.

Example:
`team_1 vs\ team_2\\\\team_2\ vs\ team_1\\`

Both the above game are same and it is a mistake to take two different game.

∴ Total number of games played by all team=
`((n * number\ of\ games\ played\ by\ each\ team)/(2)`

⇒ Total games =
`((10* 18))/(2) = 90\ games`

∴ Rana have to schedule 90 games in the Volleyball league.