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由 RAT 於 星期二 七月 04, 2006 8:44 pm
由 binglee 於 星期一 七月 03, 2006 11:06 pm
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#第一階段.先不考慮ccc.只考慮aaabbbde的排法#ed_op#br#ed_cl#(1)aaa鄰且bbb鄰=4!=24#ed_op#br#ed_cl#(2)aaa鄰且bb鄰=3!*P(4,2)=72#ed_op#br#ed_cl#(3)aa鄰且bbb鄰=3!*P(4,2)=72#ed_op#br#ed_cl#(4)aa鄰且bb鄰={(3!)*(2*2*4)+(2!*P(3,2))*(P(5,2))}=96+240=336#ed_op#br#ed_cl#(5)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#aaa鄰=#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#3!*C(4,3)=24#ed_op#br#ed_cl#
(6)aa鄰=(2!*P(3,2))*C(5,3)+(3!*2)*C(4,2)=120+72=192#ed_op#br#ed_cl#
(7)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#bbb鄰=#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#3!*C(4,3)=24#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(8)bb#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#鄰=(2!*P(3,2))*C(5,3)+(3!*2)*C(4,2)=120+72=192#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(9)a無鄰且b無鄰=全-(1)(2)(3)(4)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(5)(6)(7)(8)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#= 8!/(3!*3!)-(24+72+72+336+24+192+24+192)=1120-936=184#ed_op#br#ed_cl##ed_op#br#ed_cl#第二階段.考慮ccc排入#ed_op#br#ed_cl#(1)0#ed_op#br#ed_cl#(2)1#ed_op#br#ed_cl#(3)1#ed_op#br#ed_cl#(4)C(7,1)=7#ed_op#br#ed_cl#(5)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(7,1)=7#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(6)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(8,2)=28#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(7)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(7,1)=7#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(8)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(8,2)=28#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(9)C(9,3)=84#ed_op#br#ed_cl##ed_op#br#ed_cl#二階段合併#ed_op#br#ed_cl#=0+72+72+2352+168+5376#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#+168+5376+15456#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#=29040#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#br#ed_cl#
修正說明.第一次時漏掉(5)~(8)...#ed_op#br#ed_cl##ed_op#br#ed_cl#樓下貼的那篇連結.用排容原理方法比較好#ed_op#br#ed_cl#
(6)aa鄰=(2!*P(3,2))*C(5,3)+(3!*2)*C(4,2)=120+72=192#ed_op#br#ed_cl#
(7)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#bbb鄰=#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#3!*C(4,3)=24#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(8)bb#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#鄰=(2!*P(3,2))*C(5,3)+(3!*2)*C(4,2)=120+72=192#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(9)a無鄰且b無鄰=全-(1)(2)(3)(4)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(5)(6)(7)(8)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#= 8!/(3!*3!)-(24+72+72+336+24+192+24+192)=1120-936=184#ed_op#br#ed_cl##ed_op#br#ed_cl#第二階段.考慮ccc排入#ed_op#br#ed_cl#(1)0#ed_op#br#ed_cl#(2)1#ed_op#br#ed_cl#(3)1#ed_op#br#ed_cl#(4)C(7,1)=7#ed_op#br#ed_cl#(5)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(7,1)=7#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(6)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(8,2)=28#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(7)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(7,1)=7#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(8)#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#C(8,2)=28#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#(9)C(9,3)=84#ed_op#br#ed_cl##ed_op#br#ed_cl#二階段合併#ed_op#br#ed_cl#=0+72+72+2352+168+5376#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#+168+5376+15456#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#span id="convert151027"#ed_cl##ed_op#span class="postbody"#ed_cl#=29040#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl#
#ed_op#br#ed_cl#
修正說明.第一次時漏掉(5)~(8)...#ed_op#br#ed_cl##ed_op#br#ed_cl#樓下貼的那篇連結.用排容原理方法比較好#ed_op#br#ed_cl#
[問題]字母排列數
由 一陣風 於 星期二 五月 16, 2006 10:49 am
#ed_op#DIV#ed_cl#將a a a b b b c c c d e這11個字母排成一列，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#規定同字母不相鄰，則有幾種排列方法？#ed_op#/DIV#ed_cl#