Permutation formula:
[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]In this case:
n is the nuber of woman in the race
r is the number of woman chosen (3 as you need to know the number of possibles 3 first places combinations)
[tex]\begin{gathered} P(6,3)=\frac{6!}{(6-3)!} \\ \\ =\frac{6!}{3!} \\ \\ =\frac{1\cdot2\cdot3\cdot4\cdot5\cdot6}{1\cdot2\cdot3} \\ \\ =4\cdot5\cdot6 \\ \\ =120 \end{gathered}[/tex]Then, there are 120 first second and third place possibilities that can occur
