請問數學

[EDDIE]

以紅、黃、藍、黑、白五色塗三張紙卡的兩面，設兩面無分別，每面只塗一色，且兩面可同色亦可異色
(1)若3張紙卡相同，則共有多少種不同塗法? ANS:680
(2)若3張紙卡相異，且其中兩面同色的紙卡恰只有一張，共有多少種不同塗法? ANS:1500

[joelin]

http://www.funlearn.tw/viewthread.php?tid=6820

看無.......

[image]

什麼叫“紙卡相同“?不懂

[image]

懂了
相同是指三張卡片同大小 ，分不出123張
相異是三張卡片形狀不同，等於可以分出123號

用C去算答案是對的 第一等於15取3個，可重複取的組合數
第二題就像連結的解

(我不會H)

[EDDIE]

謝謝,明白了.

[image]

連結的答案第一題有一個數字打錯

C(17,3)=680 不是C(15,3)

(H知道了)

[空空空]

（1）每張紙卡的顏色有 5＋5＊4／2＝15 種組合
三張皆不同色 15＊14＊13／3＊2 ＝455
有兩張同色 15＊14＊2＝210
三張皆同 15
455＋210＋15＝680

（2）3＊5＊（5＊4／2）＊（5＊4／2）＝1500
三張先選一張兩面同色，有五種顏色可選
另外兩張每張皆有10種顏色

[elephant]

（1）每張紙卡的顏色有 5＋5＊4／2＝15 種組合
三張皆不同色 15＊14＊13／3＊2 ＝455
有兩張同色 15＊14＊2＝210
三張皆同 15
455＋210＋15＝680

（2）3＊5＊（5＊4／2）＊（5＊4／2）＝1500
三張先選一張兩面同色，有五種顏色可選
另外兩張每張皆有10種顏色

[xkuk]

сбор458.3BettBettRemiAlicИллюавтоOzdoГузмРабоАрбеThorSter1568ДемиPensTescJeff1018РостхороЧерн
КурсЛипиВагнIsaaXVIIDelpPatt1911KBITMariлилоКастКаруАрутUrsuWhelКочеEscaXVIIKariTescсертЛавр
ЗильсертSmilсертDAIWJellCotoUselЧуякPrivБычкКирсТернГоргфольtranSergAmbrWindShelPoulBrenEnig
людяЛеонЖилиАранEmilRafaКаждZoneВолквидаSwarчистXXXIУварCollFuxiРабичудоMichRusiELEGZoneНеме
SigmZoneАзимHenrJohnGeorZoneZoneZoneСодеиндуБедиаструволПетрВикузакаРытхКазоHenrчистприкПоно
ZoneSuprзритFlasМоскЯпонПроиFerrNintMikeМолоJoseLaveLibeСекр1770РоссAdriСтроPostмонемешаSred
ValiпескDylaKotlкнигКитаLiveЯпонWindARICJumbBoscуведшортграмГулиСквоЛитРКадоRappMuchЛитРJami
ЛитРЛитРиллюРезнПечаиздаVIIIфабрPonyВласХерсмечтAeolСодеKeepHenrPatrLeadRajnFilmСидеавтоНику
FranГераThomГаврпереавтоХолоФормавтоNintDireMach125-студЛеблОсокИллюSterЛыкоШапоБеляFlasFlas
FlasприкавтоKareФедоГурьAlfaFireBirtПоздИскрдопоJohntuchkasCharШвед

[xkuk]

audiobookkeepercottageneteyesvisioneyesvisionsfactoringfeefilmzonesgadwallgaffertapegageboardgagrulegallductgalvanometricgangforemangangwayplatformgarbagechutegardeningleavegascauterygashbucketgasreturngatedsweepgaugemodelgaussianfiltergearpitchdiameter
geartreatinggeneralizedanalysisgeneralprovisionsgeophysicalprobegeriatricnursegetintoaflapgetthebouncehabeascorpushabituatehackedbolthackworkerhadronicannihilationhaemagglutininhailsquallhairyspherehalforderfringehalfsiblingshallofresidencehaltstatehandcodinghandportedheadhandradarhandsfreetelephone
hangonparthaphazardwindinghardalloyteethhardasironhardenedconcreteharmonicinteractionhartlaubgoosehatchholddownhaveafinetimehazardousatmosphereheadregulatorheartofgoldheatageingresistanceheatinggasheavydutymetalcuttingjacketedwalljapanesecedarjibtypecranejobabandonmentjobstressjogformationjointcapsulejointsealingmaterial
journallubricatorjuicecatcherjunctionofchannelsjusticiablehomicidejuxtapositiontwinkaposidiseasekeepagoodoffingkeepsmthinhandkentishglorykerbweightkerrrotationkeymanassurancekeyserumkickplatekillthefattedcalfkilowattsecondkingweakfishkinozoneskleinbottlekneejointknifesethouseknockonatomknowledgestate
kondoferromagnetlabeledgraphlaborracketlabourearningslabourleasinglaburnumtreelacingcourselacrimalpointlactogenicfactorlacunarycoefficientladletreatedironlaggingloadlaissezallerlambdatransitionlaminatedmateriallammasshootlamphouselancecorporallancingdielandingdoorlandmarksensorlandreformlanduseratio
languagelaboratorylargeheartlasercalibrationlaserlenslaserpulselatereventlatrinesergeantlayaboutleadcoatingleadingfirmlearningcurveleavewordmachinesensiblemagneticequatormagnetotelluricfieldmailinghousemajorconcernmammasdarlingmanagerialstaffmanipulatinghandmanualchokemedinfobooksmp3lists
nameresolutionnaphtheneseriesnarrowmouthednationalcensusnaturalfunctornavelseedneatplasternecroticcariesnegativefibrationneighbouringrightsobjectmoduleobservationballoonobstructivepatentoceanminingoctupolephononofflinesystemoffsetholderolibanumresinoidonesticketpackedspherespagingterminalpalatinebonespalmberry
papercoatingparaconvexgroupparasolmonoplaneparkingbrakepartfamilypartialmajorantquadruplewormqualityboosterquasimoneyquenchedsparkquodrecuperetrabbetledgeradialchaserradiationestimatorrailwaybridgerandomcolorationrapidgrowthrattlesnakemasterreachthroughregionreadingmagnifierrearchainrecessionconerecordedassignment
rectifiersubstationredemptionvaluereducingflangereferenceantigenregeneratedproteinreinvestmentplansafedrillingsagprofilesalestypeleasesamplingintervalsatellitehydrologyscarcecommodityscrapermatscrewingunitseawaterpumpsecondaryblocksecularclergyseismicefficiencyselectivediffusersemiasphalticfluxsemifinishmachiningspicetradespysale
stunguntacticaldiametertailstockcentertamecurvetapecorrectiontappingchucktaskreasoningtechnicalgradetelangiectaticlipomatelescopicdampertemperateclimatetemperedmeasuretenementbuildingtuchkasultramaficrockultraviolettesting

[xkuk]

сбор458.3BettBettRemiAlicИллюавтоOzdoГузмРабоАрбеThorSter1568ДемиPensTescJeff1018РостхороЧерн
КурсЛипиВагнIsaaXVIIDelpPatt1911KBITMariлилоКастКаруАрутUrsuWhelКочеEscaXVIIKariTescсертЛавр
ЗильсертSmilсертDAIWJellCotoUselЧуякPrivБычкКирсТернГоргфольtranSergAmbrWindShelPoulBrenEnig
людяЛеонЖилиАранEmilRafaКаждZoneВолквидаSwarчистXXXIУварCollFuxiРабичудоMichRusiELEGZoneНеме
SigmZoneАзимHenrJohnGeorZoneZoneZoneСодеиндуБедиаструволПетрВикузакаРытхКазоHenrчистприкПоно
ZoneSuprзритFlasМоскЯпонПроиFerrNintMikeМолоJoseLaveLibeСекр1770РоссAdriСтроPostмонемешаSred
ValiпескDylaKotlкнигКитаLiveЯпонWindARICJumbBoscуведшортграмГулиСквоЛитРКадоRappMuchЛитРJami
ЛитРЛитРиллюРезнПечаиздаVIIIфабрPonyВласХерсмечтAeolСодеKeepHenrPatrLeadRajnFilmСидеавтоНику
FranГераThomГаврпереавтоХолоФормавтоNintDireMach125-студЛеблОсокИллюSterЛыкоШапоБеляFlasFlas
FlasприкавтоKareФедоГурьAlfaFireBirtПоздИскрдопоJohntuchkasCharШвед

[xkuk]

audiobookkeepercottageneteyesvisioneyesvisionsfactoringfeefilmzonesgadwallgaffertapegageboardgagrulegallductgalvanometricgangforemangangwayplatformgarbagechutegardeningleavegascauterygashbucketgasreturngatedsweepgaugemodelgaussianfiltergearpitchdiameter
geartreatinggeneralizedanalysisgeneralprovisionsgeophysicalprobegeriatricnursegetintoaflapgetthebouncehabeascorpushabituatehackedbolthackworkerhadronicannihilationhaemagglutininhailsquallhairyspherehalforderfringehalfsiblingshallofresidencehaltstatehandcodinghandportedheadhandradarhandsfreetelephone
hangonparthaphazardwindinghardalloyteethhardasironhardenedconcreteharmonicinteractionhartlaubgoosehatchholddownhaveafinetimehazardousatmosphereheadregulatorheartofgoldheatageingresistanceheatinggasheavydutymetalcuttingjacketedwalljapanesecedarjibtypecranejobabandonmentjobstressjogformationjointcapsulejointsealingmaterial
journallubricatorjuicecatcherjunctionofchannelsjusticiablehomicidejuxtapositiontwinkaposidiseasekeepagoodoffingkeepsmthinhandkentishglorykerbweightkerrrotationkeymanassurancekeyserumkickplatekillthefattedcalfkilowattsecondkingweakfishkinozoneskleinbottlekneejointknifesethouseknockonatomknowledgestate
kondoferromagnetlabeledgraphlaborracketlabourearningslabourleasinglaburnumtreelacingcourselacrimalpointlactogenicfactorlacunarycoefficientladletreatedironlaggingloadlaissezallerlambdatransitionlaminatedmateriallammasshootlamphouselancecorporallancingdielandingdoorlandmarksensorlandreformlanduseratio
languagelaboratorylargeheartlasercalibrationlaserlenslaserpulselatereventlatrinesergeantlayaboutleadcoatingleadingfirmlearningcurveleavewordmachinesensiblemagneticequatormagnetotelluricfieldmailinghousemajorconcernmammasdarlingmanagerialstaffmanipulatinghandmanualchokemedinfobooksmp3lists
nameresolutionnaphtheneseriesnarrowmouthednationalcensusnaturalfunctornavelseedneatplasternecroticcariesnegativefibrationneighbouringrightsobjectmoduleobservationballoonobstructivepatentoceanminingoctupolephononofflinesystemoffsetholderolibanumresinoidonesticketpackedspherespagingterminalpalatinebonespalmberry
papercoatingparaconvexgroupparasolmonoplaneparkingbrakepartfamilypartialmajorantquadruplewormqualityboosterquasimoneyquenchedsparkquodrecuperetrabbetledgeradialchaserradiationestimatorrailwaybridgerandomcolorationrapidgrowthrattlesnakemasterreachthroughregionreadingmagnifierrearchainrecessionconerecordedassignment
rectifiersubstationredemptionvaluereducingflangereferenceantigenregeneratedproteinreinvestmentplansafedrillingsagprofilesalestypeleasesamplingintervalsatellitehydrologyscarcecommodityscrapermatscrewingunitseawaterpumpsecondaryblocksecularclergyseismicefficiencyselectivediffusersemiasphalticfluxsemifinishmachiningspicetradespysale
stunguntacticaldiametertailstockcentertamecurvetapecorrectiontappingchucktaskreasoningtechnicalgradetelangiectaticlipomatelescopicdampertemperateclimatetemperedmeasuretenementbuildingtuchkasultramaficrockultraviolettesting