首页
登录
职称英语
A reading list for a humanities course consists of 10 books, of which 4 are biog
A reading list for a humanities course consists of 10 books, of which 4 are biog
游客
2024-01-12
37
管理
问题
A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?
选项
A、90
B、115
C、130
D、144
E、195
答案
B
解析
The requirement to select 4 books, including 2 or more biographies, means that you have to consider three cases. A student can choose 4 biographies and no novels, or 3 biographies and 1 novel, or 2 biographies and 2 novels.
Case 1: Choose 4 biographies. This case is easy, as there is only 1 way to choose all four biographies and no novels.
In the other two cases, you have to find the number of ways of choosing the biographies and the number of ways of choosing the novels and then multiply these two numbers.
Case 2: Choose 3 biographies and 1 novel. First, you need to find the number of ways of choosing 3 biographies out of 4. If you think of this as not choosing 1 out of the 4, you see that there are 4 choices. The number of ways of choosing 1 novel out of the 6 novels is 6. Therefore, the total number of choices is(4)(6)= 24.
Case 3: Choose 2 biographies and 2 novels. First, you need to find the number of ways of choosing 2 biographies out of 4. This number is sometimes called "4 choose 2" or the number of combinations of 4 objects taken 2 at a time. If you remember the combinations formula, you know that the number of combinations is
(which is denoted symbolically as
). The value of
= 6. Thus, there are 6 ways to choose 2 biographies out of 4. Similarly, the number of ways to choose 2 novels out of 6 is
= 15. Thus, the total number of ways to choose 2 biographies and 2 novels is(6)(15)= 90.
Adding the number of ways to choose the books for each of the three cases, you get a total of 1 + 24 + 90 = 115. The correct answer is Choice B.
转载请注明原文地址:https://tihaiku.com/zcyy/3355785.html
相关试题推荐
李明正在看报纸。LiMingisreadinganewspaper.
Hewasveryrudetothecustomsofficer,______ofcoursemadethingsevenworse
Hewasveryrudetothecustomsofficer,()ofcoursemadethingsevenworse.A、w
Isteachingimportant?Well,ofcourseitis.Therewasatimewhenthenece
Innocountry______Britaincanoneexperiencefourseasonsinthecourseofasi
Outofallthestudentswhoenrollinamassiveopenonlinecourse(MOOC),o
Outofallthestudentswhoenrollinamassiveopenonlinecourse(MOOC),o
Thesecourses,ifproperlyconducted,will______themindsofthestudents.A、refr
Agoodmodernnewspaperisanextraordinarypieceofreading.Itisremarkabl
They______thisnovelforfourhours.Letthemhavearest.A、arereadingB、haveb
随机试题
What’sthetalkmainlyabout?[br][originaltext]Someofthemostpractic
[originaltext]Whatcanwelearnaboutthetwospeakers?[/originaltext]A、Theydi
[audioFiles]audio_eusm_j01_127(20099)[/audioFiles]A、Howprimitivepeopleusedf
Since2007,theAmericanPsychologicalAssociation(APA)hasconductedasurve
[originaltext]M:Uh,whereamI?W:Excuseme.Doyouneedanyhelp?M:Nab,I…
社会保险是政府通过立法强制实施,由劳动者、劳动者所在的工作单位或社区以及国家三方
患者,女性,48岁。因子宫肌瘤入院拟行手术治疗。护士为使患者适应医院环境所采取的
28岁男性患者误服敌百虫后大汗淋漓,瞳孔缩小,肌肉抽搐,诊断为有机磷中毒。解救该
共用题干 男婴,7个月,近两个月来肤色苍白,食欲减退入院。生后一直人工喂养,未
下列关于建筑市场诚信行为公布的说法正确的是()。A.建筑诚信行为记录由各省、自
最新回复
(
0
)