Math and probability wasn't ever my strong side, so I need to ask for a help in calculating simple (as I assume) value. Here is situation description.
Player A throws seven times with ten-side dice (numbers in range 1-10). Writes down results and shows them to player B. Player B throws three times with the same dice.
What is the probabillity that among all ten numbers (both players) there will be no repeats - i.e. all three player B's numbers will be exactly different than all player A's numbers?
This comes from a simple game, that I've been playing. Developer of this game suggests that above mentioned situation can appear fairly often (sometimes 2-3 times per particular game) completely random. While I'm pretty sure, that probability of such situation is so extremely low, that it can't happen that often, without any changes to game random generator, to make game itself much harder to complete. In other words -- I claim that game's random generator is not that random.
Thank you in advance for any help.