Maths Permutation Combination

2014-11-01 3:51 am

A team of 14 members are going to play a football match.

a.) Find the number of ways if they are divided equally into 2 groups.
ANS: 1716

b.)-One of them quits. The remaining members are divided into 2 groups, each consists of 6 members. The member left behind will be the referee. If Alex and Billy ( two of the members) must be the two team leaders, find the number of possible ways to do this.

ANS:12012

可唔可以解釋一下點做，同埋show steps？

感激不盡！

更新1:

抱歉，有一條新問題，但希望各位能幫一幫忙！ Each class will send 5 representatives to participate in the inter-class drama competition. Q: There are 16 boys and 17 girls in S5B. If they want their drama team to consist of at least 3 girls, how many possible drama teams can be formed? Ans: 125868

更新2:

我的計法：首先抽 3 girls ： 17C3 = 680 ways 然後在剩下的30人中抽2人： 30C2 =435 ways 所以答案等於：680*435 =295800 這個計法有什麼問題？有什麼重複了？正確的方法又應該是怎樣？希望各位能幫幫忙！感激不盡！！！

回答 (1)

邊位都好

2014-11-01 3:40 pm

✔ 最佳答案

a.) Choose 7 members out of these 14 members, there are C(14, 7) ways,
that is, 3432 ways. As they can be either in the first team or the other team,
so there are only C(14, 7)/2 ways, ie. 1716 ways.

b.) Except Alex and Billy, choose 1 member for the referee, there are 11 ways,
then 5 members out of the rest 10 members to Alex's team, there are C(10, 5) ways,
that is, 252 ways. The rest are belong to Billy's team. So,
no. of possible ways is : 11 * C(10, 5) = 2772

(
the answer you provided is wrong. The only possible explanation is :
if Alex and Billy are not the members, then the no. of possible ways is,
13 * C(12, 6) = 12012
)

2014-11-02 00:43:01 補充：
There are 3 cases, (3 girls 2 boys), (4 girls 1 boy) and (all 5 are girls).
So the answer is :
17C3 * 16C2 + 17C4 * 16C1 + 17C5
= 81600 + 38080 + 6188
= 125868

你嘅方法太多重曡，例如抽出3女(F1, F2, F3)後，再在剩下抽出的2人如果包括某女生F4，
那在另一情況抽出3女(F2, F3, F4)後，再抽出女生F1的話，咁就重曡咗29次。
所以實在太多重疊了。

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