gwd 問題

treewing929 · 发表于 2012-3-2 07:09:29

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?

A.20

B.40

C.50

D.80

E.120

這條如何計算 D?謝謝大家!

treewing929 · 发表于 2012-3-2 07:30:03

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =

A.   6
B.   5
C.   4
D.   3
E.   2
答案是 B. 沒有頭緒

treewing929 · 发表于 2012-3-2 08:59:49

A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?

A.   5
B.   6
C.   7
D.   8
E.   9
這個為何是 8?? 感激!! 這類題我常常想不出答案

ericx000 · 发表于 2012-3-2 10:58:02

C5/3 people is to be selected from among 5 married couples, and then *2*2*2, because you could choose either husband or wife from each married couples.

treewing929 · 发表于 2012-3-2 18:53:42

C5/3 people is to be selected from among 5 married couples, and then *2*2*2, because you could choose either husband or wife from each married couples.

-- by 会员 ericx000 (2012/3/2 10:58:02)

謝謝你!! 其他題目呢? 有沒有人幫助? 感謝!

treewing929 · 发表于 2012-3-3 07:38:38

C5/3 people is to be selected from among 5 married couples, and then *2*2*2, because you could choose either husband or wife from each married couples.

-- by 会员 ericx000 (2012/3/2 10:58:02)

不好意思. 請問為什麼是 5C3 而不是 10C3? 不是從 10人中抽 3人嗎?
不可以 10 人是不是因為如果10人選 3人會有 COUPLE 可能被抽中?

WildeLee · 发表于 2012-3-3 09:05:05

如果C10/3的话，理论上后面就不需要*2*2*2了，因为直接从10个里面选了3个
但是，如果直接10选3的话，就存在抽中couple的可能性，因此要减去抽中couple的情况就是C10/3-C5/1*C8/1（一对couple随便搭剩下8人中的一个）=120-40=80
或者直接先从5对couple中选3对，再从中各抽取一个人，就避免了couple=C5/3*C2/1*C2/1*C2/1=80

WildeLee · 发表于 2012-3-3 09:10:54

第二题 point (-2, 1)到圆心的距离是4，point (-2, 1)在圆内，所以r>4
point (4, -3)到圆心的距离是6，在圆外，多远r<6
r又是一个整数只能为5了

coldmetal · 发表于 2012-3-3 09:13:46

A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?

A. 5
B. 6
C. 7
D. 8
E. 9
這個為何是 8?? 感激!! 這類題我常常想不出答案

设 abc 三人, 去A办公室有 abc, ab, ac, bc 四种乘以二故 8

WildeLee · 发表于 2012-3-3 09:17:53

第三题
前面那句话的意思是一个办公室空着一个办公室住3个的这种情况是允许的
于是分为两种情况来看，第一种情况：一个办公室空着一个办公室住3个=C2/1=2
第二种情况：一个办公室住两个一个办公室住一个，先把3个人分为两组，一组2个人一组1个人，分法有C3/1种，然后把两组住进两个办公室，有C2/1种。C3/1+C2/1=6
2+6=8

gwd 問題

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