please help me. I need steps. (solution at the bottom) thank you. 5 marks
2. (b) A school organized a table-tennis tournament. Any two players must play against each other. However, a player was quit after playing 3 matches and another player was absent from two matches, therefore these two players did not play against each other. If a total of 57 matches were played finally, how many players were there originally?
Solution: 2. (b) 12
maths nCr and nPr 2
2010-08-11 7:20 am
回答 (1)
2010-08-11 8:05 am
✔ 最佳答案
Let n be the original no. of players,(n-1)C2+3-2+1=57
(n-1)(n-2)/2=55
n^2-3n+2=110
n^2-3n-108=0
(n-12)(n+9)=0
n=12 or 9 (rej.)
Therefore, there are 12 players originally,
Let A be the quit player, B be the player from 2 matches
(n-1)C2 = total no. of matches played by ALL players including B but excluding A
3 = total no. of matches played by A
-2 = total no. of matches B missed
+1 because the the match that A and B did not play is counted twice (by +3 and -2)
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https://hk.answers.yahoo.com/question/index?qid=20100810000051KK02140