Answer to Question #10149 in Math for judson9

Question

Playing texas hold'em yesterday my Sweetie had a 7 and a queen in the pocket. On the board came up three sevens and two queens. Not a very likely mix. What is the likelihood of such a thing?

Thanks, Jerry

Answer 1

We have a combination of 7 cards from the deck. Total number of possible
variants is
52C7=52!/(52-7)!7!=133784560. And there is only 3 possible
variants for our situation (they differ by suit of a seven which is out). So the
probability is 3/133784560=0.00000224%