One weird thing that happened to me in high school was that the combination lock on my locker had the exact same combination as the locker next to it. It always struck me that the odds were crazy on this, but I never calculated it.
The lock was a masterlock, the kind where you have 40 options for the first number, then 39 for the second (can't use the first number again), then 39 for the 3rd number (you can use the first number again for it).
- 1/59,280 chance that two locks have the same combination. (40 * 39 * 39)
- 1/29,640 chance that any specific combination is next to mine (w/2 lockers next to mine).
That gives a 1 in (59,280 * 29,640) chance that a specific combination is next to mine? Or a 1/1,757,059,200 chance.
This seems way too high, and there's probably something I'm missing here. Any thoughts on this calculation, or what it should be?