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
10
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://www.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
YourfriendMaryaskedyouforsomeinformationaboutpreparingfortheCET-4
对计数资料进行统计描述的主要指标是A.平均数 B.相对数 C.标准差 D.
排水泵站且承泄区水位变幅较大时,为了减少工程量和工程造价,需要设()。A、进水池
下列关于我国国家审计总目标的表述,正确的是( )。A.真实性是指财政财务收支以
2017年,S市服务业小微样本企业总体实现营业收入105.39亿元,同比增长3.
(2021年上半年真题)“做人,做中国人,做现代中国人”这一教育目的提出者是A.
影响企业支付能力的因素有( )。A.劳动分配率 B.销货劳动生产率 C.损
人在每一瞬间,将心理活动选择了某些对象而忽略了另一些对象。这一特点指的是注意的(
延胡索的功效有A.活血 B.消积 C.行气 D.凉血 E.止痛
以下关于乡村主要任务表述错误的是()A.乡村振兴,产业兴旺是重点 B.乡
最新回复
(
0
)