# How many 24 hands are there?

Submitted by admin on Fri, 06/19/2009 - 14:56

Edie Cappy writes:

How many combinations to make a 24 hand?

Can any mathematically inclined readers answer this?

## As far as I know, the 24

As far as I know, the 24 hands are 33339, 44447, 66663, 7777A, 45566, 44566, 44556, 67788, 77889. If you take into account the different suits, there are 4 ways to get each of the first 4 listed, and 144 ways to get each of the other 5. For example: in the 33339 hand, there is only one way to choose the 3s, and 4 ways to choose the 9. This gives 4 ways to get the 33339 hand. In the 45566 hand, there are 4 ways to choose the 4, 6 ways to choose 5s and 6 ways to choose 6s. This gives 4x6x6=144 ways to get that particular 24 hand. The others use the same argument. This makes 4x4+5x144=736 different 24 hands. If you care about what card is cut then the figure changes by a factor of 5. For example: if you consider 3h 3d 3c 3s with 9h cut to be a different hand than 3h 3d 3c 9h with 3s cut, the number of 24 hands will be 5x736=3680. I will run a program to check it for sure because I am not sure if I got all of the base hands right, though I am confident.