1. How many different colored cubes are there in which each face is colored either red or white or blue?
2. Prove: Let G be a finite group of permutations acting transitively on the finite set X, where |X|>1. There exists at least one element g Ԑ G having no fixed point on X, i.e., such that g(x) doesn't equal to x for all x Ԑ X.
Math Problems
2011-03-09 8:29 pm
回答 (3)
2011-03-12 3:03 am
✔ 最佳答案
Q1: Ans: 3+24+30=57種case1: 1 colors => C(3,1)*1=3
case2: 2 colors => C(3,2)*8= 24
RWWWWW => 1*2=2
RRWWWW => 2*2=4
RRRWWW => 2 (RR填對面,與RRR全相鄰)
共2+4+2=8種
case3: 3 colors => 22種
RWWBBB =>3!* 3 (WW對面or相鄰, 3!是RWB交換)
RWBBBB => 3* 2 (RW對面or相鄰)
RRWWBB => 6 (RR對面有兩種, RR相鄰有4種)
共 18+6+6=30種
2.
設X={1,2,3,...,n}, n>=2
取g=(123..n) [circle permutation g(1)=2, g(2)=3, ..., g(n)=1]
則g(x)與x絕不會相等
2011-03-12 1:28 am
原來統計老兵大大是大學老師!
2011-03-11 7:08 am
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https://hk.answers.yahoo.com/question/index?qid=20110309000051KK00348