The count changes with every spot selection
A reader asking how many number combinations exist in keno is usually standing at a terminal or a paper slip, deciding how many spots to mark. The honest first answer is that there is no single number. The count depends on two variables: how many numbers you choose to play, and how many numbers the house draws from its pool. Change either variable and the combination count changes with it.
Keno is a lottery-style draw game. A player marks a set of numbers on a ticket, the house draws a larger set from the same pool, and the player is paid according to how many of their marked numbers appear in the draw. The combinatorial question sits entirely in the first step: given a pool of a fixed size, how many different ways can a player mark a given number of spots.
Because the answer is a function of two inputs rather than a stored fact, this article explains the mechanism and gives the reader a way to compute the figure for any keno format they encounter. No venue-specific numbers are supplied here, and none are invented.
The counting rule behind every keno ticket
The number of ways to choose a set of spots from a larger pool is a binomial coefficient, commonly written as "n choose k". In keno terms, n is the size of the number pool the game uses, and k is the number of spots the player marks. The formula counts every unordered subset of size k that can be drawn from a pool of n numbers.
The binomial coefficient is calculated as n! divided by (k! × (n − k)!), where the exclamation mark denotes a factorial: the product of all whole numbers from that value down to 1. For example, 5! equals 5 × 4 × 3 × 2 × 1, which is 120. The formula deliberately ignores the order in which numbers are marked, because a keno ticket does not care whether a player marked 7 before 23 or 23 before 7. A set is the same set either way.
This single rule answers every version of the question. If a keno game uses a pool of 80 numbers and a player marks 10 spots, the number of possible 10-spot tickets is "80 choose 10". If a different game uses a pool of 70, the figure becomes "70 choose 10". If the same 80-number game allows a 6-spot ticket, the figure becomes "80 choose 6". The mechanism does not change; only the inputs do.
Why the draw size does not change the ticket count
A common point of confusion is whether the house's draw size affects the number of possible player combinations. It does not. The house draws a set of winning numbers from the same pool, but the player's ticket is fixed before that draw happens. The number of possible tickets is determined only by the pool size and the number of spots marked.
What the draw size changes is the probability structure: how likely a given number of matches is, and therefore how the pay table is built. But the combinatorial question "how many different tickets can I mark" is answered before the draw size enters the picture. A reader who wants the count of possible tickets should hold the draw size aside and focus on the pool and the spot count.
That said, the draw size matters for a different question: how many different draw outcomes exist. That is a second binomial coefficient, "n choose d", where d is the number of balls the house draws. A reader should be clear which of the two counts they want, because the two numbers answer different things.
Worked example, labelled as an example
To show the mechanism without asserting any real venue's format, take a hypothetical keno game with a pool of 80 numbers and a player marking 10 spots. The number of possible 10-spot tickets is "80 choose 10". This is 80! divided by (10! × 70!). The computation is large but mechanical, and any scientific calculator or spreadsheet can evaluate it.
If the same hypothetical game draws 20 numbers, the number of possible draw outcomes is "80 choose 20". That is a different and much larger figure. The ticket count and the draw count are separate quantities, and conflating them is the most common error in keno combination questions.
The point of the example is not to hand the reader a memorised figure. It is to show that the answer is always a binomial coefficient with clearly identified inputs. A reader who can identify the pool size and the spot count can compute the answer for any keno game they meet.
What changes the count across keno variants
Keno formats differ across jurisdictions and platforms, and those differences change the inputs to the binomial coefficient. The table below lays out the variables that determine the count, and what stays fixed regardless of format.
| Variable | What it does to the combination count | Where the reader finds it |
|---|---|---|
| Number pool size (n) | Larger pool means more possible tickets for the same spot count | Game rules or pay table for the specific keno product |
| Spots marked (k) | More spots means more possible tickets, up to a peak, then fewer | Ticket layout or terminal selection screen |
| House draw size (d) | Does not change ticket count; changes draw outcome count | Game rules or help screen |
| Order of marks | No effect; combinations are unordered sets | Not applicable |
The peak in the middle row is a property of binomial coefficients: for a fixed pool, the count is largest when k is close to half of n, and smallest when k is 1 or n. A reader who wants the maximum possible ticket count for a given pool should look at the spot count nearest half the pool size.
Where the authoritative number for a specific game lives
No article can state a single keno combination figure that applies everywhere, because the pool size and permitted spot range are set by the operator or the jurisdiction and printed in the game's own documentation. The authoritative source is the rules document or pay table for the specific keno product the reader is looking at.
That document states the pool size, the minimum and maximum spots a player may mark, and the draw size. With those three numbers, the combination count is computable. Without them, any figure would be a guess dressed up as a fact, and this article does not do that.
A reader who is looking at a physical ticket should check the printed rules on the back or the terminal help screen. A reader looking at an online keno product should open the game's rules or info page. The channel is the product's own published rules, not a third-party summary.
What to confirm before you rely on a count
Before using any keno combination figure, confirm three things. First, the exact pool size the game uses. Second, the exact number of spots you intend to mark, because the count changes with every spot. Third, whether the figure you are looking at is a ticket count or a draw outcome count, since the two are routinely confused.
Also confirm whether the game permits duplicate numbers or ordered picks. Standard keno does not: every number is unique and order is irrelevant. If a variant deviates from that, the binomial coefficient no longer applies and a different counting rule takes over. The product's rules page will say which model it uses.
Finally, remember that the combination count describes how many tickets exist, not how likely any ticket is to win. Probability is a separate calculation that involves the draw size and the pay table. A large combination count tells a reader nothing about their expected return.
FAQ
Is there one fixed number of keno combinations?
No. The count depends on the pool size and the number of spots marked. A game with an 80-number pool and a 10-spot ticket has a different count from the same game with a 6-spot ticket, and a different count again from a game using a 70-number pool. The answer is always a binomial coefficient with those two inputs.
Does the number of balls drawn change how many tickets I can mark?
No. The draw size affects the number of possible draw outcomes and the probability of matching a given number of spots, but it does not change how many different tickets a player can mark. The ticket count is set by the pool size and the spot count alone.
How do I find the combination count for a specific keno game?
Open the game's published rules or pay table and note the pool size, the spot count you want, and the draw size. Compute "pool choose spots" for the ticket count, and "pool choose draw size" for the draw outcome count. Any scientific calculator or spreadsheet can evaluate these.
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This article is general information about how these mechanics work. It is not legal advice and not a recommendation to gamble or to use any particular operator. Availability and legality differ by jurisdiction — check the rules that apply where you are.