Each little floret within the whole inflorescence contains both sexual organs inside that little tube. A quick dissection of one will show you. Best to select a flower that is young, with the outer ring of florets just opened. That's when (and where) there is the most pollen and the stigma is receptive. As the inner rings of florets open, the older ones are no longer viable. As those little florets continue to open, they provide less and less nectar to reward the pollinators, and produce less pollen.

You'll need something smaller than a paint brush to do the job. Good luck, and have fun!