SOLUTION: A six-team hockey league has a schedule requiring each team to play each of the other teams 9 times. How many games will be played in total?

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Question 1147127: A six-team hockey league has a schedule requiring each team to play each of the other teams 9 times. How many games will be played in total?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

Playing one time each with the other, they play %286%2A5%29%2F2 = 15 times.


Playing 9 times each with the other, they play 9*15 = 135 times, in all.    ANSWER


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Count the total number of games that each team plays; then, since that counts each game twice, divide by 2:

(number of teams) times (number of opposing teams) times (number of times per season)
6*5*9 = 270
then divide by 2
270/2 = 135

OR, to be a bit more sophisticated mathematically....

(2) Determine the number of pairings and multiply by the number of times per season that each pairing occurs:

(6 choose 2) times (number of times per season)
6C2 * 9 = 15*9 = 135