更新1:
Please prove if Peter is correct.
Permutation
2010-12-12 4:50 pm
For (m + n) boys, where m ≥ n > 1, to be seated in a row, Peter said the no. of arrangement is (m + 1)Pn x m! if the n boys must be separated. Is Peter correct? If no, what should be the no. of arrangement?
回答 (2)
2010-12-12 5:08 pm
✔ 最佳答案
First arrange the m boys in a row, there is m! waysThen insert the n boys among the m boys()M()M()M()M()…()M()There are m+1 positions to insert these n boys in order that they are separatedThere are (m+1)Cn ways to choose these n positionsThere are n! ways to arrange the order of the n boysSo total number of ways = (m!)[(m+1)Cn](n!)= (m+1)Pn × m!
2010-12-13 1:11 am
收錄日期: 2021-04-23 23:23:21
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https://hk.answers.yahoo.com/question/index?qid=20101212000051KK00218