eight students are competing for a blue, red, and yellow ribbon for their agriculture project. how many…

Explanation:

Step1: Identify the problem type

This is a permutation problem. We want to find the number of ways to select 3 students out of 8 for the 3 - colored ribbons when order matters. The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be selected.

Step2: Substitute values into the formula

Here, $n = 8$ and $r=3$. So $P(8,3)=\frac{8!}{(8 - 3)!}=\frac{8!}{5!}$.

Step3: Expand the factorials

We know that $n!=n\times(n - 1)\times\cdots\times1$. So $\frac{8!}{5!}=\frac{8\times7\times6\times5!}{5!}$.

Step4: Simplify the expression

The $5!$ in the numerator and denominator cancels out, leaving us with $8\times7\times6=336$.

Answer:

336