How Many Full House Hands Are There?

There are exactly 3,744 full house combinations in a standard 52-card deck, built from 156 distinct rank patterns. A full house is three cards of one rank plus two of another — “trips over a pair” — and counting them is a clean exercise in combinatorics that also explains why the hand sits where it does on the rankings ladder. Here’s the math, step by step, with every number verified.

The exact count: 3,744 combinations

To build a full house you make four independent choices. Multiply the number of ways to make each:

Step	Choice	Ways
1	Pick the rank for the three of a kind	13
2	Pick 3 of that rank’s 4 suits — C(4,3)	4
3	Pick a different rank for the pair	12
4	Pick 2 of that rank’s 4 suits — C(4,2)	6

Multiply them together:

13 x 4 x 12 x 6 = 3,744

That’s the total number of distinct five-card full house hands in the deck. The trips rank and the pair rank must differ (step 3 uses 12, not 13), because using the same rank for both would need five cards of one rank — impossible in a single deck.

The 156 distinct rank patterns

If you ignore suits and only care about the names — “aces full of kings,” “twos full of aces,” and so on — you count differently. Pick the trips rank (13 ways) and then a different pair rank (12 ways):

13 x 12 = 156

So there are 156 uniquely named full houses. Each one, like “queens full of jacks,” corresponds to 4 x 6 = 24 specific card combinations (four ways to choose the trips suits, six ways to choose the pair suits). And indeed 156 x 24 = 3,744, which confirms both numbers agree.

The odds of being dealt one

There are 2,598,960 possible five-card hands, so the probability of a full house on the deal is:

3,744 / 2,598,960 = 0.00144, or about 1 in 694.

That rarity is exactly why a full house ranks so high — fourth of the ten hands. Compare it to its neighbors on the ladder:

Hand	Combinations	Roughly 1 in
Four of a kind	624	4,165
Full house	3,744	694
Flush (non-straight)	5,108	509

A full house is rarer than a flush (so it beats one) but more common than four of a kind (so it loses to quads). The counts line up perfectly with the ranking order — poker’s ladder is just rarity in disguise.

Why the multiplication works

Each of the four steps is independent, so the counting principle says you multiply. The C(4,3) = 4 in step 2 is the number of ways to leave out one suit from the trips; the C(4,2) = 6 in step 4 is the number of two-suit pairs. Because choosing the trips doesn’t restrict which suits the pair uses (the ranks are different), nothing overlaps and no combination is counted twice. That clean independence is what makes the full house one of the easiest premium hands to count. For what the hand actually is and how it plays, see full house meaning.

A common miscount to avoid

People often try to count full houses as “choose 2 ranks out of 13,” which gives C(13,2) = 78, and then get confused. The mistake is treating the two ranks as interchangeable. In a full house the trips rank and the pair rank play different roles: “aces full of kings” and “kings full of aces” are two distinct hands, so you must count ordered pairs of ranks — 13 x 12 = 156 — not unordered ones. The 78 figure would only be right if the trips and pair were the same size, which they never are. Once you keep the trips-first ordering straight, the rest of the arithmetic falls out cleanly.

Ranking full houses against each other

With 156 named full houses, ties between two full houses do happen, and they’re settled by the trips first. Aces full of kings is the single best; twos full of threes is the worst. The full method — higher trips wins, pair only breaks ties — is covered in how to compare full houses.

Bottom line

There are 3,744 full house combinations in a 52-card deck, arising from 156 distinct rank patterns, and you’ll be dealt one roughly once every 694 hands. The count comes straight from 13 x 4 x 12 x 6, and it explains the hand’s place on the ladder: rarer than a flush, more common than quads. Dig into more poker counting at the odds and math hub, or review the full ladder at the hand rankings hub.