eight students are competing for a blue, red,...
eight students are competing for a blue, red, and yellow ribbon for their agriculture project. how many different ways are there to present those ribbons if the order matters?\n56\n336\n6,720\n8,064
Answer
# Explanation:
## Step1: Identify permutation formula
We use the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the number of students (8) and $r$ is the number of ribbons (3).
## Step2: Calculate factorial values
$n!=8! = 8\times7\times6\times5\times4\times3\times2\times1$, $(n - r)!=(8 - 3)!=5!=5\times4\times3\times2\times1$. Then $P(8,3)=\frac{8!}{5!}=\frac{8\times7\times6\times5!}{5!}$.
## Step3: Simplify the expression
Canceling out the $5!$ terms, we get $P(8,3)=8\times7\times6 = 336$.
# Answer:
336