數學難題(Combination),麻煩請比意見

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2011-12-11 16:36:00 補充：
Consider all vowels as one group, then this group together with the 6 consonant are 7 groups. The total number for these 7 groups are 7! ways.

2011-12-11 16:37:24 補充：
Among these ways, there are cases that the 7 vowels are at the front and at the end. Consider the arrangements of the consonants 6! for each of these cases, there are indeed 2x6! ways

2011-12-11 16:39:36 補充：
Hence total number of ways (not considering the arrangement of the vowels) = 7! - 2x6!
Considering the arrangement the vowels, there are (7! - 2x6!)(7!/4!2! - 6!/4!)
=7!X(7!/4!2!-6!/4!) - 6!(7!/4!2! - 6!/4!)X2