What is the combination probability?

Diddums said:
Digilocks are ornamental, on most of them you can simply shine a light at the right angle and see which buttons were pressed due to the marks left by fingers. Add to this the fact that the sequence is irrelevant and they're pointless.
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I think saying they're pointless is a bit much. That is what this thread has tried to determine.

@dowie thinks that you have a 0.16% chance of success to gain entry without knowing the code, in spite of no number repetitions and an irrelevant character order. That's hardly pointless.
 
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