By my back of an envelope calculations, there are 14 playable races in the PHB. For classes, once the options are unlocked by level 3 at the latest, there are 46 available choices. There are 13 backgrounds.
I make that 8372 possible combinations.
If I post a character a day I’ll be busy for the next 23 years.
Looks like I have an answer to the #rpgaday question about why I’ll be doing 20 years from now after all.