1. Define the Variables and Points

Let:
- $r=$ Number of red chips (2 points each)
- $b=$ Number of blue chips (4 points each)
- $g=$ Number of green chips (5 points each)

The product of the point values is given as $\mathbf{1 6 , 0 0 0}$. We can write this as:

$$
\(2^r \times 4^b \times 5^g=16,000\)
$$

2. Factorize the Product

First, let's break down 16,000 into its prime factors:

$$
\(\begin{gathered}
16,000=16 \times 1,000 \\
16,000=2^4 \times\left(10^3\right) \\
16,000=2^4 \times(2 \times 5)^3 \\
16,000=2^4 \times 2^3 \times 5^3 \\
16,000=2^7 \times 5^3
\end{gathered}\)
$$

3. Set up the Equation

Now, substitute the prime factors back into our chip equation. Note that $4^b$ can be rewritten as $\(\left(2^2\right)^b\)$ or $\(2^{2 b}\)$ :

$$
\(\begin{gathered}
2^r \times 2^{2 b} \times 5^g=2^7 \times 5^3 \\
2^{r+2 b} \times 5^g=2^7 \times 5^3
\end{gathered}\)
$$

4. Solve for the Number of Chips

From the equation above, we can equate the exponents for each prime base:
1. For base 5: $\(g=3\)$
2. For base 2: $\(r+2 b=7\)$

The problem states that the number of blue chips equals the number of green chips ( $b=g$ ).
Since $g=3$, then $b=3$.

Now, substitute $b=3$ into the second equation to find $r$ :

$$
\(\begin{gathered}
r+2(3)=7 \\
r+6=7 \\
r=1
\end{gathered}\)
$$


There is 1 red chip in the selection.