(13) Place 6 small balls of the same shape (2 red, 2 yellow, and 2 blue) randomly into 3 boxes, with exactly 2 balls in each box. Let $\xi$ be the number of boxes in which the balls are of the same color. Find the distribution of $\xi$.
13 From the problem, we know that $\xi$ can take $0, 1, 3$.
$$
\begin{array}{l}
P(\xi=3)=\frac{1}{5} \cdot \frac{1}{3}=\frac{1}{15} \\
P(\xi=1)=3 \cdot \frac{1}{5} \cdot\left(1-\frac{1}{3}\right)=\frac{2}{5} \\
P(\xi=0)=1-P(\xi=3)-P(\xi=1)=\frac{8}{15} .
\end{array}
$$