If you care about ordered or unordered counts you can use nCr or nPr. But If you want a few in a certain order and a few unordered is there a general approach?

For example imagine you have 6 red balls and 5 blue balls and you select 3 balls.

How large is the set of balls where the first is blue and the remaining two are red.

I determined it to be 25.

If order didn't matter you could have (6 red choose 2 red) * (5 blue choose 1)=75

Then by symmetry, a third must start with blue. So 75/3=25 RRB BRR RBR

I'm wondering if there is a more general way to think about this problem.