Question

a track team has 10 runners, but only 3 can participate in a relay race, each running a different leg of the race. how many ways can the coach choose and arrange 3 runners for the race?
_{10}p_{3} = ?

Explanation:

Step1: Recall permutation formula

Permutation formula: $P(n,k)=\frac{n!}{(n-k)!}$ where $n=10$, $k=3$.

Step2: Calculate factorial values

$10! = 10×9×8×7!$, $(10-3)! =7!$.

Step3: Simplify and compute

$P(10,3)=\frac{10×9×8×7!}{7!}=10×9×8=720$.

Answer:

720