@Floppy Yes. if you throw them all together, you have 6^6 total possible outcomes. 1..6 can be arranged in 6! ways. So you have 720 out of 46,656 possibilities that match your desired outcome. That is 1.54%.

So if you want for something to keep you busy, throw a single dice and try to get 1..6 in order. Wrong number: start over. Now you can expect to need about 46,656 throws.

[Edit: I mistakenly added an extra factor of 6 to the "serial" version]