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14.35: a baseball league has nine teams. during the season, each of the nine teams plays exactly three games with each of the other teams. what is the total number of games played?

Sagot :

Answer:

One team must play 8 games 3 times equals 24 games

One team must play 24 games

But each game uses 2 teams so there are 12 games in all

Or 9 * 24 / 2 = 108 games

Check: If there were 3 teams then one team must play

2 games 3 times  for a total of 6 times so the total of games played will be six for each team or 18 games, but each game uses 2 teams so the total of games is nine:  1-2, 2-3, 1-3 (each team has played its opponent once) - 3 * 3 = 9

T = number of teams in league

(T - 1)    1 team plays each other once

(T - 1) * T  each team has played 1 game for entire league

(T - 1) * T / 2   total games to be played for 1 game each

G *  (T - 1) * T / 2     where G is number of games