I am trying to understand the bulls and cows document, Page $6$, equivalences. Can someone please tell me what author means when he says $\boldsymbol{ {}^n C_k \times {}^n P_k}$ like ${}^4 P_0 \times {}^4 C_0$ and ${}^4 P_1 \times {}^4 C_1$?
$$\sum_{n=\max(0, p-(d-u))}^{n=p} {}^u P_n \cdot {}^p C_n = \sum \frac{u!}{(u-n)!} \cdot \frac{p!}{(p-n)! \cdot n!}$$
$$\begin{array}{ccrcr} {}^4 P_0 \cdot {}^4 C_0 &=& 1 \cdot 1 &=& 1 \\ {}^4 P_1 \cdot {}^4 C_1 &=& 4 \cdot 4 &=& 16 \\ {}^4 P_2 \cdot {}^4 C_2 &=& 12 \cdot 6 &=& 72 \\ {}^4 P_3 \cdot {}^4 C_3 &=& 24 \cdot 4 &=& 96 \\ {}^4 P_4 \cdot {}^4 C_4 &=& 24 \cdot 1 &=& 24 \\ \hline &&&&209 \end{array}$$
$4P2=4\cdot 3=12, 4C2=4\cdot 3/2=6$,so$4P2 \times 4C2=12\times 6=72$