組合覆蓋問題

（原標題：概率問題） 
來源: 馨尹 於 06-12-17 00:56:20
 已知13個數字中任選3個數字的組合是286組，13個數字中任選6個數字的組合是1716組，請問選6個數字的組合中最少幾組就可以包含所有選3的組合？  

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Deuss:

35個可以，不知能否更少

split 13 elements into 7 groups: [1,2],[3,4]...[11,12],[13].

form size 6 groups by picking all 3-combinations from these 7, (add any one additional element if [13] is used). There are C(7,3)=35 of them.