Let $X_1$, and $X_2$ and $X_3$ be chosen independently from the set $\{0, 1, 2, 3, 4\}$, each value being equally likely. What is the probability that the arithmetic mean of $X_1, X_2$ and $X_3$ is the same as their geometric mean?
- $\frac{1}{5^2}\\$
- $\frac{1}{5^3}\\$
- $\frac{3!}{5^3}\\$
- $\frac{3}{5^3}$