全国15亿人口中选1000个代表有多少种选法？

快速组合数C（N，K）=N*（N-1）*（N-2）*...*(N-K+1)/1*2*3*...*K  的求法：

   Function ZDGYS(ByVal x As Long, ByVal y As Long) As Long 'GET Greatest Common Divisor最大公约数
 
   Dim TEMP As Long
    If x > y Then TEMP = x: x = y: y = TEMP   'LET X < Y
   Do
      TEMP = y Mod x
      If TEMP = 0 Then ZDGYS = x: Exit Function
      y = x
      x = TEMP
  Loop
   End Function
Sub CALC(ByVal N As Long, ByVal K As Long, Optional ByRef CNK As String) '计算C（N，K），赋值给CNK
Dim XYS() As Integer, x() As Integer, y() As Integer, result() As String, i As Long, j As Long, T As Long, TEMP As Long, stimer As Double
If N < 0 Or N < K Then Exit Sub
stimer = Timer
If K = N Or K = 1 Then CNK = N: GoTo R '特殊情况
If N > 0 And K = 0 Then CNK = 1: GoTo R '特殊情况
If K > N - K Then K = N - K '减少计算量
Dim NN() As Long, NK() As Long
ReDim NN(1 To K)
ReDim NK(1 To K)
For i = 1 To K
NN(i) = N + 1 - i ' N*(N-1)*(N-2)*....*(N+1-K)
NK(i) = i ' 1*2*3*...*K
Next

For i = K To 1 Step -1
             For j = 1 To K
            TEMP = ZDGYS(NK(j), NN(i)) '最大公约数
            If TEMP > 1 Then '消除分子分母
               NN(i) = NN(i) / TEMP
               NK(j) = NK(j) / TEMP
               End If
            Next
Next

ReDim x(1)
ReDim XYS(1)
x(1) = 1 '初始化数组
XYS(1) = 1
T = 1

Do While Not T > K

TEMP = Len(CStr(NN(T)))
ReDim y(1 To TEMP)
For i = 1 To TEMP
y(i) = Val(Mid(NN(T), TEMP + 1 - i, 1))
Next
ReDim XYS(1 To UBound(x) + UBound(y))
For i = 1 To UBound(x)
For j = 1 To UBound(y)
XYS(i + j - 1) = XYS(i + j - 1) + x(i) * y(j) '模拟乘法运算
Next
Next
For i = 1 To UBound(x) + UBound(y) - 1 '进位
TEMP = XYS(i) / 10
XYS(i) = XYS(i) Mod 10
XYS(i + 1) = XYS(i + 1) + TEMP
Next
T = T + 1
x = XYS
If x(UBound(x)) = 0 Then ReDim Preserve x(1 To UBound(x) - 1) '第一位为零则去掉之

Loop

ReDim result(1 To UBound(x)) '逐位赋值
For i = 1 To UBound(x)
result(i) = x(UBound(x) + 1 - i)
Next

CNK = Join(result, "") '最后结果
R:
Debug.Print "C(" & N & "," & K & ")=" & CNK & vbCrLf & "用时 "; Timer - stimer & " 秒, 结果大约为 " & Val(Left(CNK, 3)) / 100 & "* 10^" & Len(CNK) - 1
Erase x() '释放
Erase y()
Erase XYS()
Erase result()
Erase NN()
Erase NK()

End Sub

Private Sub Command1_Click()
CALC 1500000000, 1000
End Sub

 

 

C(1500000000,1000)=30652804367164696580061245618584644612627630767867968160482287207505578854118075767413733341865113545827821943234215925381601476838491502713562101051308121811886256344264074095500443454498544782873527381232953591608839778443126863125303594776637408010065945137971003022970106087272779912095118673993148835415545404803408210359936057541641298321398866367630909780954427950260602677841356572015384593028076391922880188863454695625613158555189739103273043693186054292522757402389201949262458783982625369769215639665513120651343627077305247225448215405511745177315577297307995592278944000912129608635572003811892730638646576505559665098287067901804492021447447275828527448463319437263974332506979369648426322521012083011115417734792185803613847776098673007574058102010392545564626748974852860654213922561671313738154819315936146389699558632939168101222776477404052002491162770708016843923192174292119830692530203631071406591557820008413480936874626325481432195805380233658534174129959183937867662826991079111
338507834850334729288527369247878587832565479208744508778338876845312482987364108498465104568456246126301664867675212989415452257963231582428804132453530623562038287815118381775031194128075371634249125005163175363459748867914155909874673736671257895290315504998299550045865237426434834900678181142251825976824066859247763393966728415101293183767884565520685140354199404573267540148178613083039288640368764932196092260612808432688740318168177149884264936965681432808552602506769960231167314402042115391322928445848804527619718942273029739119754679079466440615744683934345683854846607341007539932315717364854225714347670890166770915776776243078592968724832489687527728645194872553456998869305207865806227228240462763947538604009461323117527793289745018918680050158833377256878342226038335968075073066708948751926064101932688708070972742976746669773522500626362218897275189840528789502160913361730351366579932326949751303046239529917281431024867799141200833929055039117446235095261319287039924501955885408786864766666179804050
926238297570352362160646695473979572080274723182393467252406938755835973585538888233140836639673055810280530161047565105056191259402557546062663149807820850721607832667883835853491798687285433469973723070029887151224892374554667132810263246741920398381560995586116435336668086735996210380651185950181222288773122498950468782425732304340361291059389453644565588619918495101003681448457650276701709851748681473864319718504684039251604015610508150552147153808743465905683130916303237016638713958685021075266783472002051065502419194601235929294444041936017137491251351327293306795207718070253412158539452418227263212189992863000083749471357436062471359873115691304279442807157134670115889000449540459077189604149293330863116234937585596100863199359470190862668063710752295922314349843213145637598520454977206161737311181275038945492592107963547180908095567677268276647414212537107884627846628529110671588643375513826567593228681751623648914212833098504187516701899089836341651632877201830938439864542029138356501030414803306920
447442494403172023855874827652475829549179429277923966103280437285008533655739559815237810160800404271399529345607321632407618302218506087747281711816275952385300123419119651812539626008479518803800204241415723861161475364403266589079446760547415461785658842813934872809441606838372946069290650323137211372623387643292062185604875098174848114827946543780012495836176514887528611865682171001390146194237358933818961231577169742945244631925175731309409301203657814823561195573417039611685481744639624779650478031797010310193910143720654230005835120916672556896141697397124339430683527827346088199310425977296050580090894283395562704660146243992392610035169484756111583491872862842868457498966835895427651725999857936637086391945848855014479550565464117387609584985877716361649333274656753939030226599302839809864418684901638821616862306126650440096166767836408098656108833121089444398772930568736130647757518593668394884786266077836647532339577756373420434996413495897686581823977660804033665502785475102224252209292029993611
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993811980475311411632351682411636284449523363102094638794683659899605243052500175768769099173718367066781811361348638425178173533659503191787287397210467403797148018620943140078863571236739256270024107992839957976629695925235827394515603914164183723922107475389399917198511707432424313798630024979383132858351486262556758911527206975222453347937597508581111638702889231077175618142416071510061074549357572130933606480227128227922241716100276558744960483990492564330618193933962874467321168691702843418522393313197859657767931876154079079628597519811667958999436727218235364130406291499386395626751121774249109113139023137242731007972509781943833703136500894934240004229538784683585221465034084172567082331416819337218490736760012020257897928012089371742387533535843560376935269710997788468956524236901127076130233737094320642223543634031712270479693894837408024549625851428164388516669349329127033123394379811722300561676344810618825484416094886382203022666376818249128029887498208543129659288646346274769309292407404574993
6608908558954975144280515042437103513526943923346637991231240111666845924976878803784724718010351062368178879274540425781148703984672314559414795767769357321073222899722903734370283198049596503724417629404981774693732136715506926958567040649893166041510601704826598030208663351081485700207580107291827140144496139095464493330834978911758605670606624144954404663833872654567200762263525195723339349006395584852284826376552648716276636192737185771244752744819887086709751962025613217186000000
用时 9.03125 秒, 结果大约为 3.06* 10^6608