After 2 hours of writing down numbers on a paper bag I have come to the conclusion that there are 1,351,262,201,047,401,204,160,762,000,386,537,239,347,200 (43 digits) combinations of armors in minecraft. This includes all 20 base armor pieces (leather, iron, chain, gold, diamond). Dyed leather armor. Enchanted armor. And every possible name you can put on an armor piece. There is a total of 49,305,584 combinations without enchants or names, 30,986,038,385,462,467,200 with enchants, and 1,351,262,201,047,401,204,160,762,000,386,537,239,347,200 with names

Thanks for reading, this took 2 hours of sitting on my bed doing math- WHILE ON VACATION. These are the lengths I'm willing to go to to avoid going outside.