It seems I'd have been number 35, but if I had been born 2 days earlier I'd have avoided it. Seems rather random.
As I understand it, everyone eligible for service was assigned a number between 1-366, after a birthday was drawn at random to go with each number. If your birthday was matched with an early number it made it more likely you'd be drafted than if your birthday was up in, like, the 300s. So one day early or late could make a big difference. I think something like half the numbers were called up at the height of the war.