but rearrangements don't count and we can use any from the set for any slot, repeats ok, repeats not 'degenerate'?
rolling dice, say i roll one and get six, then roll again and get six, the probability of what just happened occuring is (1/6)X(1/6) as to say (1/6)^2. The Twitter naming scheme allows repeats, etc. so essentially it is just rolling a 52 sided die 5 times for the first 5 slots. If we are to allow the string to exist elsewhere in the filename, that does provide more possibilities, but I don't feel it is necessary to count those. see image and yahtzee example.
"There is a 1 in 62^5 (1 in 916132832) chance the first 5 digits of the 15 digit file name will be ‘DOITQ’." that is the same math but with the 10 digits. I think just the statement of 1 in 916132832 is better for most purposes than moving into probabilities that are not perfectly definable. Just my opinion. 1 in 62 the hands make a Q if i read that correctly? Makes a person stop reading it.