PP-T1-PS-43

[yiyiyi]

A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

(A) 16
(B) 24
(C) 26
(D) 30
(E) 32

ans: E

[sunnyblue13s]

(8*6*4)/3! = 32 - 排列

OOO → 一個蘿蔔一個坑，求組合!!

[pauline_chiou]

請問這裡除以3!是為什麼??

[Huang Hsin-Yi]

請問這裡除以3!是為什麼??

因為 abc acb bac bca cba cab 是同一種組合

[pauline_chiou]

突然腦筋轉不過來.....謝謝Huang Hsin-Yi ^^

提供另外一個想法
committe中不能有couple的組合即 "全部的組合-committe中有couple的組合"
8!/3!5!-4*6
=56-24
=32
(4*6代表將couple視為一個人，有4個coule，另外一個committe則為其他六個人選一個)

[xie_dongbo]

(8*6*4)/3! = 32 - 排列



OOO → 一個蘿蔔一個坑，求組合!!

請問.比較一下
44. 5871-!-item-!-187;#058&004763※
A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior officers and 1 junior officer, how many different committees are possible?

(A) 8
(B) 24
(C) 58
(D) 80
(E) 210

如果用一個蘿蔔一個坑
OOOO→ (6*5*4)*4/4! 答案就錯了
是我哪裡犯錯呢?

附上這一題
【答案】D

【思路】C(6,3)XC(4,1)
=20X4=80
謝謝