There are eight boys and six girls who are members of the trumpet section in the band. From the members of the trumpet section, a quintet is being formed. If the quintet must consist of three boys and two girls, how many quintets are possible?
First, we consider how many ways there are to choose three boys from eight. There are $8$ choices for the first boy, $7$ for the second, and $6$ for the third. However, because the boys are indistinct from one another, we have overcounted, and must divide by $3 \cdot 2$. Similarly, there are $6 \cdot 5$ ways to choose the two girls, divided by $2$ for overcounting. Thus, there are $\frac{8 \cdot 7 \cdot 6 \cdot 6 \cdot 5}{3 \cdot 2 \cdot 2} = \boxed{840}$ possible quintets.