Question

Springdale Junior High has two students, Ashley and Taylor, that qualified for the regional track meet in the 800 meter dash. The final race has only four spots available. Both Ashley and Taylor earned a spot in the final.

Answer 1

I assume you want to know a permutation about how many ways they can be in the final set-up.

Order matters, which is why this is a permutation.

Formula: P(n, r) = $\frac{n!}{(n-r)!}$

where the permutation is $n^{P} k$, with P for permutation.

Plug in:

4!/(4-2)!
4!/2!
(1 x 2 x 3 x 4)/1 x 2
(3x4)/1
= 12

12 ways.