supposethatm+nballs,ofwhichnareredandmareblue,arearrangedinalinearorderinsuchawaythatall(m+n)!possibleorderingsareequallylikely.ifwerecordtheresultofthisexperimentbyonlylistingthecolorsofthesuccessiveballs,s

Question

suppose that m+n balls,of which n are red and m are blue,are arranged in a linear order in such a way that all (m+n)!possible orderings are equally likely.if we record the result of this experiment by only listing the colors of the successive balls,show that all the possible results remain equally likely.
Consider any one of the (n+m)!possible ordering and note that any permutation of the red balls among themselves and of the blue balls among themselves does not change the sequence of colors.as a result ,every ordering of colorings corresponds to different orderings of the n+m balls,so every ordering of the colors has probability /(n+m)!of occurring.终于打完了...
答案没看懂,翻译一下也成.主要是n!代表的是红球和篮球怎么排列?

Answer 1

噢,很简单,题目让你排列m+n个球,然后求有多少种相同的排列方法
总排列方法是(m+n)!
相同的总共为n!*m!,差不多是这个意思吧