Number of two pair distinct hands

Question

Well I'll try to be brief, reviewing the statistics about how to achieve a double pair I came to the conclusion that for each kicker of each card, (that in total 11 for each one), there are a total of 1584 possible hands for a single card, and if we count all the cards we get a total of 123552, but there is still a loose 858 that is the total of different hands, how do I get to that number? Can someone give me an example?

Summarizing the possible combinations to achieve a single couple are 6

1. K ♠ K ♥
2. K ♥ K ♣
3. K ♦ K ♠
4. K ♦ K ♥
5. K ♣ K ♦
6. K ♣ K ♠

Then this way • 12 pairs x 12 cards: 144 double pairs • 144 double pairs x 11 kickers: 1584 double pairs for a single card

Answer 1

For a five-card hand, first choose the two ranks that you want for your two pair. There are 13 x 12 / 2 = 78 ways to do this.

Then, for each pair, choose the two suits: 6 each.

Then pick the other card that's neither of the pair ranks: 44 choices (11 ranks x 4 suits).

This gives 78 x 36 x 44 = 123,552 two-pair hands.