What is the probability of getting a hand (10 cards) in gin rummy that has no two cards that go together? [i.e. no pairs of the same number and no two cards in a row of the same suit]
We've been playing a lot of gin rummy over the past year during Covid-19 closures, and I haven't gotten a hand like that yet, but I know such hands are possible because I can easily construct one.
Fifty years ago I might have been able to solve some probability problems using permutations and combinations, but that was fifty years ago; furthermore I doubt if I could have solved this one even then.
[yes, I googled this and couldn't find an answer there in the first few pages of results]