由 雞腿飯 於 星期四 二月 03, 2005 12:48 am
aa,d,iii,m,nn,s,tt,r,o
任取四個字,求其組合數
f=(1+x+xx+xxx)*(1+x+xx)^3*(1+x)^5, 求其x^4項係數
f=(1-x^4)/(1-x)*(1-x^3)^3/(1-x)^3*(1-x^2)^5/(1-x)^5
=(1-x^4)(1-3x^3+...)(1-5x^2+10x^4-...)/(1-x)^9
=(1-5xx-3xxx+9xxxx)/(1-x)^9
其x^4項係數=C(4+8,8)-5C(2+8,8)-3C(1+8,8)+9
=12*11*10*9/24-5*10*9/2-3*9+9
=495-225-27+9
=252
排列數
f=(1+x+xx/2!+xxx/3!)*(1+x+xx/2!)^3*(1+x)^5, 求其x^4項係數
...... 瘋了 ^_^!!!
F=(e^x-xxxx/24)*(e^x-xxx/6-xxxx/24)^3*(e^x-xx/2-xxx/6-xxxx/24)^5, 求其x^4項係數
let A=e^x
F=(A-xxxx/24)*(AAA-AAxxx/2-AAxxxx/8+...)*(AAAAA-AAAA*5(xx/2+xxx/6+xxxx/24)+AAA*10*(xx/2)^2+...)
==AAAAA*(A-xxxx/24)(A-xxx/2-xxxx/8)(AA-5A(xx/2+xxx/6+xxxx/24)+5xxxx/2)
==AAAAA*A(A-(xxxx/24+xxx/2+xxxx/8)(AA-5A(xx/2+xxx/6+xxxx/24)+5xxxx/2)
==AAAAAA*(AAA-AA(xxxx/24+xxx/2+xxxx/8+5xx/2+5xxx/6+xxxx/24)+A5xxxx/2)
=A^9-A^8(5xxxx/24+4xxx/3+5xx/2)+A^7*5xxxx/2)
x^4項係數
=9^4/4!-5/2*8^2/2!-4/3*8/1!-5/24+5/2
排列數=(x^4項係數)*4!
=6561-60*32-32*8-5+60
=4440
不知對不對
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