Question

GRE数学求帮助！Three typists work for four companies

Three typists work for four companies, each company has one document, what is the probability that three typists all receive documents?
多谢大神解答！

Answer 1

四家公司给三个人文件一共可能的情况有3×3×3×3＝81种，
全给一个人做，3种。
给两个人做，不考虑文件考虑给哪两个人有3种，一个人做1个另一个人3个4×2＝8种，一个人做2个另一个人2个6种，一共3×(8＋6)＝42种。
给三个人做，两个人分别做一个，一个人做两个，不考虑文件考虑做的人有3种，做两个文件有6种，剩下两个给两个人有2种，一共有3×6×2＝36种。
所以你要求的概率为36/81＝4/9