首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
The letters C, I, R, C, L, and E can be used to form 6-letter strings such as CIRCLE or CCIRLE. Using these letters, how many d
The letters C, I, R, C, L, and E can be used to form 6-letter strings such as CIRCLE or CCIRLE. Using these letters, how many d
admin
2022-10-18
37
问题
The letters C, I, R, C, L, and E can be used to form 6-letter strings such as CIRCLE or CCIRLE. Using these letters, how many different 6-letter strings can be formed in which the two occurrences of the letter C are separated by at least one other letter?
选项
A、96
B、120
C、144
D、180
E、240
答案
E
解析
This can be solved by using the Multiplication Principle. The answer is m × n, where m is the number of ways to choose the 2 suitable positions in which to place the C’s and n is the number of ways in which to place the 4 remaining letters in the 4 remaining positions.
The value of m can be found by a direct count of the number of suitable ways to choose the 2 positions in which to place the C’s. In what follows, each * denotes one of the 4 remaining positions.
There are 4 possibilities when a C is in the first position:
There are 3 more possibilities when a C is in the second position:
There are 2 more possibilities when a C is in the third position:
There is 1 more possibility when a C is in the fourth position:
Therefore, w = 4 + 3 + 2 + 1 = 10.
Alternatively, the value of m can be found by subtracting the number of non-suitable ways to place the C’s (i.e., the number of consecutive positions in the string) from the number of all possible ways to place the C’s (suitable or not).
This gives m = 15 - 5 = 10, where 15 =
is the number of all possible ways to place the C’s ("6 choose 2") and 5 is the number of non-suitable ways to place the C’s (shown below).
The value of n is equal to the number of ways to place the 4 remaining letters into 4 positions, where order matters and the letters are selected without replacement. Thus, n = 4! = 24.
Therefore, the answer is m×n = 10×24 = 240.
The correct answer is E.
转载请注明原文地址:https://jikaoti.com/ti/BzzYFFFM
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
HarrietBeecherStowehadpouredherheartintoheranti-slaverybook,"UncleTom’sCabin".Butneithershenorherfirstpubl
WhatdowemeanbyaperfectEnglishpronunciation?Inone【C1】______therearemanydifferentkindsofEnglishastherearespeak
Whensheheardthebadnews,she______completely.
Withtheflowers______everywhere,theparklooksbeautiful.
AwarenessWeeks(认知宣传周)havebecomearegularpartofBritain’sculturallandscapeoverthepastfewyears.Theystartedbackin1
Hegotuptotheroof______aladder.
Frankfurt,Germany,isoneofthemost______populatedregionsinWesternEurope.
Iftheareaofasquarewithsidesoflength8centimetersisequaltotheareaofarectanglewithawidthof4centimeters,wh
Whatisthesmallestpossiblecommonmultipleoftwointegerswhicharebothgreaterthan50?
Eventhoughmostuniversitiesretaintheroyaltiesfromfacultymembers’inventions,thefacultymembersretaintheroyaltiesfr
随机试题
氨气与()接触能发生自燃,极易爆炸。
患者,2周前左下肢皮肤划破,1周前突然畏寒、发热,3d来咳嗽、气急,伴右侧胸痛。胸片检查示右侧肺炎伴液(脓)气胸。最好应用的抗生素为
医生处方中对饮片产地提出要求的药名有()。
对开展投资顾问业务而言,下列属于客户的重要的非财务信息是()。
某企业2008年度发生以下业务:以银行存款购买将于2个月后到期的国债500万元,偿还应付账款200万元,支付生产人员工资150万元,购买固定资产300万元。假定不考虑其他因素,该企业2008年度现金流量表中“购买商品、接受劳务支付的现金”项目的金额为(
业主大会议事规则是()组织、运作的规程,需要由业主共同决定。
火车A过隧道,从车头进入隧道到车尾离开隧道共用时60秒,随后与迎面开来的另一列火车B相遇,两车速度相同,火车B的长度是A的1.5倍,两车从车头相遇到车尾分开共用时5秒。问:火车B从车尾进入隧道到车头离开隧道,要用时多少秒?
职业教育是指受教育者获得某种职业或生产劳动所需要的职业知识、技能和职业道德的教育。根据上述定义,下列现象不属于职业教育的是:
巴金的()包括了《家》《春》《秋》三部小说。
孙中山所说的“社会革命”是指()
最新回复
(
0
)