Question

There are 7 boys and 5 girls in a youngsters’ club. A committee of 3 boys and 2 girls is to be chosen. How many different possibilities are there?

Answer 1

$N=\begin{pmatrix} 7 \\ 3\end{pmatrix}\cdot\begin{pmatrix} 5 \\ 2\end{pmatrix}=\\ =\cfrac{7! } {3! \cdot(7-3)! } \cdot \cfrac{5! } {2! \cdot(5-2)! }=\\ =\cfrac{5\cdot6\cdot7}{2\cdot3}\cdot\cfrac{4\cdot5}{2}=\\=350.$