21. (2004 National College Entrance Examination, Tianjin Paper) From 4 boys and 2 girls, 3 people are randomly selected to participate in a speech contest. Let the random variable $\xi$ represent the number of girls among the 3 selected people.
(I) Find the distribution of $\xi$;
(II) Find the mathematical expectation of $\xi$;
(III) Find the probability that "the number of girls $\xi \leqslant 1$ among the 3 selected people".
21. ( I ) $\xi$ may take the values $0,1,2, P(\xi=k)=\frac{C_{2}^{*} \cdot C_{4}^{3-k}}{C_{6}^{8}}, k=0,1,2$. Therefore, the distribution of $\xi$ is:
\begin{tabular}{|c|c|c|c|}
\hline$\xi$ & 0 & 1 & 2 \\
\hline$P$ & $\frac{1}{5}$ & $\frac{3}{5}$ & $\frac{1}{5}$ \\
\hline
\end{tabular}
(II) $E \xi=0 \times \frac{1}{5}+1 \times \frac{3}{5}+2 \times \frac{1}{5}=1$.
(III) $P(\xi \leqslant 1)=P(\xi=0)+P(\xi=1)=\frac{4}{5}$.