I made this problem myself. Is it correct?

Permutation example: So far, there are 12 generations of Doctors. A different actor played each. For example, the 1st was William Hartnell, the 2nd was Patrick Troughton, the 3rd Jon Pertwee, the 4th Tom Baker, and so on. What if the 1st Doctor were Tom Baker, and the 2nd was Matt Smith? How many different orders can the Doctors be in? (You can't repeat, so you must do 12!)

There would be 479,001,600 ways you can order up the 12 Doctors.

Question

I made this problem myself. Is it correct?

Permutation example: So far, there are 12 generations of Doctors. A different actor played each. For example, the 1st was William Hartnell, the 2nd was Patrick Troughton, the 3rd Jon Pertwee, the 4th Tom Baker, and so on. What if the 1st Doctor were Tom Baker, and the 2nd was Matt Smith? How many different orders can the Doctors be in? (You can't repeat, so you must do 12!)

There would be 479,001,600 ways you can order up the 12 Doctors.

amistre64 · Answer

matt smith is the 13th doctor; as was explained in the 'the time of the doctor' episode.