Permutation Question

Question

A class has 6 students randomly divided into two teams A and B. what is the probability that the three sunners in team A will come first second and third?

 

Will the answer be 3!/6! or (3!3!)/6! ?

Answer 1

First, let's assume that each team consists of 3 RUNNERS.  Then what's the probability that all of team A are victorious, in the sense of coming in first, 2nd or 3rd in the race, in other words, team B is shut out from the award of ribbons or medals.

 

I think that the answer is 3C3 ÷ 6C3 = 1 / [6! / (3!3!)] = 1/20