Math

QuestionIn a league of 6 teams where each team plays every other team 3 times, how many total games are there? Use G=3×(62)G = 3 \times \binom{6}{2}.

Studdy Solution

STEP 1

Assumptions1. The baseball league consists of6 teams. . Each team plays each of the other teams three times.
3. A game is counted as one game, regardless of which team is considered the "home" team and which the "away" team.

STEP 2

First, we need to find the total number of games that one team plays. This can be done by multiplying the number of other teams by the number of times each team plays the others.
Gamesperteam=(Numberofteams1)timesNumberofgamesagainsteachteamGames\, per\, team = (Number\, of\, teams -1) \\times Number\, of\, games\, against\, each\, team

STEP 3

Now, plug in the given values for the number of teams and the number of games against each team to calculate the number of games per team.
Gamesperteam=(61)times3Games\, per\, team = (6 -1) \\times3

STEP 4

Calculate the number of games per team.
Gamesperteam=times3=15Games\, per\, team = \\times3 =15

STEP 5

Now that we have the number of games per team, we can find the total number of games in the league. This can be done by multiplying the number of games per team by the number of teams. However, this will count each game twice (once for each team), so we need to divide by2.
Totalgames=(GamesperteamtimesNumberofteams)/2Total\, games = (Games\, per\, team \\times Number\, of\, teams) /2

STEP 6

Plug in the values for the number of games per team and the number of teams to calculate the total number of games.
Totalgames=(15times6)/2Total\, games = (15 \\times6) /2

STEP 7

Calculate the total number of games.
Totalgames=90/2=45Total\, games =90 /2 =45There will be45 games played in the league.

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