Deck of cards statistics


New member
Jan 7, 2019
Good day mathematicians, hope you're well, just trying to create my own card game, but struggling with the statistics of it all, to be able to order the hands.
So the game will have 20 cards (out of a full 52) in play at a time, and the best poker hands will win, essentially, without going into too much detail of the game.

So with there being 20 cards, there is a possibility of;
10 pairs,
6 three of a kinds,
4 five card tricks.

Now I was never any good at statistics, so I'm hoping someone who is good, is willing, and able to help me out here.

The two that I know for sure are the first and last.
The first being a single pair.
And the last being Four Royal Flushes.
Obviously there is a correct order for the ones that would go in the middle, and there would be a lot to go there, but I don't even know where to start.

If you've read this and can help, feel free to message me directly, although I am currently travelling in India, so may not have WiFi! And also on different time zones, I'll get back to you ASAP.

If you've read this and can't help, also feel free to message me, don't know what about.. Maybe you just want to know if penguins have knees... Or maybe you just can't work out why there's a letter 'd' in the word fridge, but not in the word refrigerator.

Thank you so much in advance, wish you all a pleasant day.