Question

algebra i b-cr
complete
1 2 3 4 5 6
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?
○ 56
○ 336
○ 6,720
○ 8,064

Explanation:

Step1: Identify permutation scenario

We have 8 students, choosing 3 distinct ribbons where order matters, so we use permutations. The formula for permutations is $P(n,k)=\frac{n!}{(n-k)!}$, where $n=8$ (total students) and $k=3$ (ribbons to award).

Step2: Calculate factorial values

First, compute $n!=8!=8\times7\times6\times5!=40320$, and $(n-k)!=(8-3)!=5!=120$.

Step3: Compute permutation value

Substitute into the formula:
$P(8,3)=\frac{8!}{(8-3)!}=\frac{8\times7\times6\times5!}{5!}=8\times7\times6=336$

Answer:

336