jmc

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.