Question

in a spelling bee, 8 finalists compete to win 1st to 3rd place. how many different ways could these top 3 positions be filled?

\\( _8p_3 = ? \\)

Explanation:

Step1: Recall permutation formula

Permutation formula: $P(n,k)=\frac{n!}{(n-k)!}$ where $n=8,k=3$.

Step2: Calculate factorial values

$8!=8×7×6×5!$, $(8-3)!=5!$.

Step3: Simplify and compute

$P(8,3)=\frac{8×7×6×5!}{5!}=8×7×6=336$.

Answer:

336