Permutaions&combinations1
2010-12-20 4:58 am
In a badminton tournament, any 2 players must play agaist each other twice. However, a player was quit after playing 4 matches due to injury. If a total of 60 matches were played finally, how many players were there originally?
回答 (1)
2010-12-20 5:13 am
✔ 最佳答案
Supppose that there were n players originally, then original no. of games that have to be played is:2[1 + 2 + 3 + ... + (n - 1)] = n(n - 1)
So when a player quitted after playing 4 games, the no. of games will be reduced by 2(n - 1) - 4 = 2n - 6 since he/she originally had to play 2(n - 1) games.
So we have:
n(n - 1) - (2n - 6) = 60
n2 - 3n - 54 = 0
(n - 9)(n + 6) = 0
n = 9 or -6 (rej)
參考: 原創答案
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101219000051KK01144