How many 24 hands are there?

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.

Cribbage

Please show me how 66663 equals 24. Been playing Cribbage for more than 50 years and never experienced anyone counting this as 24 until recently. Would appreciate clarification.

Thank you.

66663 = 24

663 = 15 of course and that can be done 6 ways with 4 6's = 12 pts, then you have 6*4 = 12 points giving you 24 pts.

To demonstrate this we have 6-1, 6-2, 6-3, 6-4 and 3
6-1 + 6-2 + 3 = 15-2
6-1 + 6-3 + 3 = 15-4
6-1 + 6-4 + 3 = 15-6
6-2 + 6-3 + 3 = 15-8
6-2 + 6-4 + 3 = 15-10
6-3 + 6-4 + 3 = 15-12

Ther is 12 @15s. Six pairs of

Ther is 12 @15s. Six pairs of 6s and a 3.
4 of a kind is 12

Any three cards

Any three cards that equal 15, like 771 or 663 and if you have quads you will have 24. If it takes 4 cards then you will have 20 if you have quads. 99996 etc.

four 24 hands

Have you ever heard of four people getting a 24 hand because of the cut? A six was cut. Do you know what he odds of that happening are? -James from Canada