Hey, you'll get another chance... in like fifty more weeks.
Not exactly. You get a ticket for that specific year, and when you redeem that ticket it gives you a random car for that year. It isn't pre-determined, either, so if you get the ticket and don't like the car you get, if you had backed up your save before redeeming the ticket you can use it again for a chance at a different car. I've noted, however, that some cars seem to come up more frequently than others. For example, with the '67 ticket, the GT40 Mark IV and Miura come up a lot, but the Ferrari 330 P4 hasn't came up after dozens of times of redeeming the ticket.