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*2. Similarly, there are 6*5 ways to choose the two girls, divided by 2 for overcounting. Thus, there are (8*7*6*6*5)/(3*2*2)=840 possible quintets.
