YLL討論網

由 **qeypour** 於星期一二月 27, 2006 11:53 pm

piny 寫到:
qeypour 寫到:#ed_op#DIV#ed_cl##ed_op#FONT face=Verdana#ed_cl#6不同物分給X1~X8共8人,X1~X6每人至多1個的分法有幾種? #ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl#
#ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有六人有一物→C(6,6)*C(6,6)*6!*2^0=4320#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有五人有一物→C(6,5)*C(6,5)*5!*2^1=8640#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有四人有一物→C(6,4)*C(6,4)*4!*2^2=21600#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有三人有一物→C(6,3)*C(6,3)*3!*2^3=19200#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有二人有一物→C(6,2)*C(6,2)*2!*2^4=7200#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有一人有一物→C(6,1)*C(6,1)*1!*2^5=1152#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有零人有一物→C(6,0)*C(6,0)*0!*2^6=64#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#共62176種#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#解釋X1~X6有四人有一物→C(6,4)*C(6,4)*4!*2^2#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#六人中選四人出來，六物中選四物出來，所以前兩項為相乘，此四物再排列，最後二物，每物都有二個人可以給。#ed_op#/DIV#ed_cl##ed_op#P#ed_cl#

#ed_op#/P#ed_cl##ed_op#P#ed_cl# #ed_op#/P#ed_cl##ed_op#P#ed_cl#基本上您的解法是正確的#ed_op#/P#ed_cl##ed_op#P#ed_cl#只不過第一項要更正為720#ed_op#/P#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

由 **piny** 於星期一二月 27, 2006 11:28 pm

qeypour 寫到:#ed_op#DIV#ed_cl##ed_op#FONT face=Verdana#ed_cl#6不同物分給X1~X8共8人,X1~X6每人至多1個的分法有幾種? #ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl#

#ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有六人有一物→C(6,6)*C(6,6)*6!*2^0=720#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有五人有一物→C(6,5)*C(6,5)*5!*2^1=8640#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有四人有一物→C(6,4)*C(6,4)*4!*2^2=21600#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有三人有一物→C(6,3)*C(6,3)*3!*2^3=19200#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有二人有一物→C(6,2)*C(6,2)*2!*2^4=7200#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有一人有一物→C(6,1)*C(6,1)*1!*2^5=1152#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有零人有一物→C(6,0)*C(6,0)*0!*2^6=64#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#共58576種#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#解釋X1~X6有四人有一物→C(6,4)*C(6,4)*4!*2^2#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#六人中選四人出來，六物中選四物出來，所以前兩項為相乘，此四物再排列，最後二物，每物都有二個人可以給。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#謝謝qeypour大大指教！答案已更正！ ^_^#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

由 **qeypour** 於星期一二月 27, 2006 11:05 pm

#ed_op#DIV#ed_cl##ed_op#FONT face=Verdana#ed_cl#6不同物分給X1~X8共8人,X1~X6每人至多1個的分法有幾種? #ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl#

YLL討論網

發表回覆

+ / -檢視主題

Re: [問題]分法幾種

Re: [問題]分法幾種

[問題]分法幾種

(請將產生的程式碼，剪貼至上方文章區！)
[quote="qeypour"][quote="piny"][quote="qeypour"]#ed_op#DIV#ed_cl##ed_op#FONT face=Verdana#ed_cl#6不同物分給X1~X8共8人,X1~X6每人至多1個的分法有幾種? #ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl#[/quote]#ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有六人有一物→C(6,6)C(6,6)6!2^0=4320#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有五人有一物→C(6,5)C(6,5)5!2^1=8640#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有四人有一物→C(6,4)C(6,4)4!2^2=21600#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有三人有一物→C(6,3)C(6,3)3!2^3=19200#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有二人有一物→C(6,2)C(6,2)2!2^4=7200#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有一人有一物→C(6,1)C(6,1)1!2^5=1152#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#X1~X6有零人有一物→C(6,0)C(6,0)0!2^6=64#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#共62176種#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#解釋X1~X6有四人有一物→C(6,4)C(6,4)4!2^2#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#六人中選四人出來，六物中選四物出來，所以前兩項為相乘，此四物再排列，最後二物，每物都有二個人可以給。#ed_op#/DIV#ed_cl##ed_op#P#ed_cl#[/quote]#ed_op#/P#ed_cl##ed_op#P#ed_cl# #ed_op#/P#ed_cl##ed_op#P#ed_cl#基本上您的解法是正確的#ed_op#/P#ed_cl##ed_op#P#ed_cl#只不過第一項要更正為720#ed_op#/P#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl# [/quote]