The number of trailing 0s in 6000! is 1498
➥ The number of digits in 6000 factorial is 20066.
➥ The factorial of 6000 is calculated as below: 6000! = 6000 • 5999 • 5998 • 5997 • 5996 ... 3 • 2 • 1
Not quite that bad - if song selection is truly random, it’s “only” one chance in 36,000,000, assuming the co-worker also has 6000 songs on his device. The chance that device A will play song X at any time is 1 in 6000. The chance that device B will play song X at any (same or other) time is 1 in 6000. Now if you want to include the chances that song X prior to that was not played on either device A or B for a specific very large number of plays, it gets very complicated very fast!
At any given time there is a one in 6,000 chance that the same song is playing on both. Period.
If it plays 15 four minute songs every hour that means it happens on average every 400 hours, or every 10 forty hour work weeks.
The odds of it being a rare song are longer but it probably happens at least once or twice a year.