nPr and nCr (5m)

用戶90882

2010-08-07 4:45 am

Please help me. Please show steps.

1. There are 12 S5 students and 10 S6 students. 3 to 5 students are choosen among them to form a team for a competition. If the team must have 2 S6 students, how many ways are there to form the team?

2. There are 12 boys and 18 girls in the Chinese Language club. How many ways are there to select 3 students to be the club representatives given that only one of them is a boy?

3. In a soccer league, any 2 teams must play against each other twice in one season. There are 16 teams in the league for this season. How many soccer matches will be played?

Solutions :
1. 13 140
2. 1 836
3. 240

Thank you. 5 marks

更新1:

Corrections: Solutions for Q1 - 13 410

回答 (1)

用戶2053

2010-08-07 5:15 am

✔ 最佳答案

1)2 S6 student from 10 have 10C2 = 45 ways ,1 or 2 or 3 S5 students from 12 have (12C1 + 12C2 + 12C3) = 12 + 66 + 220= 298 waysTotal 45 * 298 = 13410 ways. (Not 13 140 ?)
2)(12C1)(18C2) = 1 836 ways
3)

Any 2 teams must play against each other : 16C2

TWICE : x 2 16C2 x 2 = 240 matches

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