Question

某赛事中,3男2女分到3个场馆,每个场馆都有人且有一个场馆恰好有一男一女的概率为?

Answer 1

3男2女分到3个场馆,每个场馆都有人且有一个场馆恰好有一男一女的概率为

(C(5,2)*C(3,2)*C(3,2)-C(2,2)*C(3,2)*P(3,3))/3^5

=(10*3*3-3*6)/243

=72/243

=8/27

或:

(P(5,5)*P(3,3)/(P(2,2)*P(2,2)*P(2,2))-C(3,1)*P(3,3)*P(2,2)/P(2,2))/3^5

=(90-18)/243

=72/243

=8/27