Question

There are 6 woman running in a race. How many first second and third place possibilities can occur?

Answer 1

Permutation formula:

`P(n,r)=(n!)/((n-r)!)`

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)

`\begin{gathered} P(6,3)=(6!)/((6-3)!) \\ \\ =(6!)/(3!) \\ \\ =(1\cdot2\cdot3\cdot4\cdot5\cdot6)/(1\cdot2\cdot3) \\ \\ =4\cdot5\cdot6 \\ \\ =120 \end{gathered}`

Then, there are 120 first second and third place possibilities that can occur