Leaving just one carrot to go to seed will produce enough seeds for you and your extended family. In fact, you could probably feed the neighbourhood. One carrot will produce thousands of seeds.
I've added the photograph of the carrot top 'bush'. In another couple of weeks, the ends will come out in white flowers. That is when I'll cut off the branch, invert it in a paper bag, and hang it up to dry. In a month's time, I'll have all the seeds I need!