PNRs: 6 ALPHA characters, hence 26^6 = 308,915,776
Ticket #, 10 numbers (after 001) = 10^10 = 10,000,000,000 (10 Billion)
With 2016 computer technology and super fast search capabilities, why have two different systems associated with a reservation? [Admittedly, remembering 6 characters is nicer than 10 digits], adding one more character to a PNR, would allow 26^7 = 8,031,810,176 (8 Billion).
Didn't USAir, use numbers and letters for their PNRs?
^ is the exponent symbol
A single PNR may have multiple tickets as well as non air travel items (eg hotel rooms, car hire, etc.).
If you have a few hundred spare dollars then the Reservations Services Manual and the Ticketing Handbook (both IATA books) are an interesting read.