[考題] 102南科實中數學科考題疑義? 填充Q.2
填充第二題:設有A、B、C 三艘渡船,每艘一次至多可搭載四人且不得有空船。今有六人
欲同時乘船渡河,其中恰有一對夫婦,若欲安全過渡,且該夫婦又必須同船
,幾種渡法:
我的算法:先假設夫婦乘A船,n(a,b,c)表示A船,B船,C船所承載的人數為a,b,c時的
渡法數,則夫婦乘A船安全過渡的方法數
=4^3-n(6,0,0)-n(5,1,0)-n(5,0,1)-n(4,2,0)-n(4,0,2)-n(2,0,4)
-n(2,4,0)-n(3,3,0)-n(3,0,3)=4^3-1-5-5-C4取2-C4取2-1-1-C4取3-C4取3
=64-1-4-4-6-6-1-1-4-4=33
夫婦乘B船,C船也分別有33種渡法 所以共99種
南科公佈的答案是150 我覺得答案好像有誤 有去考的朋友願意分享一下嗎? 謝謝
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