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

We need to count the number of the ways to be selected 3 boys from 7 and 2 girls from 5. The order does not matter, so we count the number of combinations without repetition:

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