Question

How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?

Answer 1

$N=\begin{pmatrix} 12 \\ 4\end{pmatrix}\cdot\begin{pmatrix} 9 \\ 3\end{pmatrix}=\\ =\cfrac{12! } {4! \cdot(12-4)! } \cdot \cfrac{9! } {3! \cdot(9-3)! }=\\ =\cfrac{9\cdot10\cdot11\cdot12}{2\cdot3\cdot4}\cdot\cfrac{7\cdot8\cdot9}{2\cdot3}=\\=41580.$