How Many Combinations Are in a 6/55 Lotto?
A clear, step-by-step answer using real combinatorics — not an approximation. We'll work through the exact formula, show the calculation in full, and compare a 6/55 format directly against SA Lotto, PowerBall, and Daily Lotto so the numbers mean something practical.
Total possible combinations in a 6/55 lotto — and therefore the jackpot odds, 1 in 28,989,675.
1. The Combination Formula Explained
Lottery combinations are calculated using the mathematical concept of "combinations," written as C(n,r) — read as "n choose r." It tells you how many different ways you can select r items from a total pool of n items, where the order doesn't matter (picking 3, 17, 42 is the same ticket as picking 42, 3, 17).
Where n! means "n factorial" — n × (n−1) × (n−2) × ... × 1
For a 6/55 lotto, n = 55 (the total number pool) and r = 6 (how many numbers are drawn), giving us C(55,6).
2. Step-by-Step Calculation for 6/55
Rather than calculating the full factorials of 55 and 6 (which would involve enormous numbers), the formula simplifies neatly for lottery combinations:
- C(55,6) = (55 × 54 × 53 × 52 × 51 × 50) ÷ (6 × 5 × 4 × 3 × 2 × 1)
Multiply the 6 largest numbers from 55 downward on top, and 6! (720) on the bottom.
- Numerator: 55 × 54 × 53 × 52 × 51 × 50 = 20,872,566,000
This is the total number of ordered arrangements of 6 numbers from 55.
- Denominator: 6! = 720
This accounts for the fact that order doesn't matter — there are 720 ways to arrange any 6 chosen numbers.
- 20,872,566,000 ÷ 720 = 28,989,675
The final, exact number of unique combinations in a 6/55 lotto.
3. What This Means for Your Odds of Winning the Jackpot
Since there's exactly one winning combination among all 28,989,675 possible combinations in a 6/55 draw, your odds of matching all 6 numbers with a single ticket are exactly 1 in 28,989,675. Every one of those 28,989,675 combinations has precisely the same probability of being drawn — there's no combination that's more or less likely than any other.
4. How 6/55 Compares to SA Lotto (6/52)
South Africa's main Lotto uses a 6/52 format — a slightly smaller number pool than 6/55. Fewer total numbers to choose from means fewer possible combinations, and therefore somewhat better jackpot odds:
| Format | Total Combinations | Jackpot Odds |
|---|---|---|
| 6/55 | 28,989,675 | 1 in 28,989,675 |
| SA Lotto (6/52) | 20,358,520 | 1 in 20,358,520 |
The difference comes entirely from the pool size — 3 fewer numbers to choose from in SA Lotto's format reduces the total combinations by roughly 30%.
5. How 6/55 Compares to PowerBall and Daily Lotto
| Format | Total Combinations | Jackpot Odds |
|---|---|---|
| 6/55 (e.g. some international lotteries) | 28,989,675 | 1 in 28,989,675 |
| SA Lotto (6/52) | 20,358,520 | 1 in 20,358,520 |
| SA PowerBall (5/50 + 1/20) | 2,118,760 × 20 = 42,375,200 | 1 in 42,375,200 |
| Daily Lotto (5/36) | 376,992 | 1 in 376,992 |
SA PowerBall's dual-pool structure (5 main numbers from 50, plus a separate PowerBall from 20) produces the longest odds of the group, even though its main pool alone has fewer combinations than a 6/55 format. Daily Lotto's smaller 5/36 format has dramatically fewer combinations than any of the 6-number games, which is why its jackpot odds are so much shorter.
6. Odds by Match Count in a 6/55 Format
Matching fewer than all 6 numbers is naturally easier, and the odds improve substantially as the required match count drops:
| Numbers Matched | Winning Combinations | Approx. Odds |
|---|---|---|
| 6 numbers (Jackpot) | 1 | 1 in 28,989,675 |
| 5 numbers | 294 | 1 in 98,604 |
| 4 numbers | 17,640 | 1 in 1,643 |
| 3 numbers | 368,480 | 1 in 79 |
Calculated using C(6,k) × C(49,6−k) ÷ C(55,6), where k is the number of matched numbers.
7. Is a 6/55 Lotto Available in South Africa?
No. None of South Africa's National Lottery games use a 6/55 format. SA Lotto is 6/52, PowerBall uses a 5/50 main pool plus a separate 1/20 PowerBall, and Daily Lotto is 5/36. A 6/55 format does exist in some international lotteries — for example, the Philippines' Grand Lotto uses this exact matrix — but it isn't offered by Ithuba in South Africa.
8. Practical Meaning for Players
- Understanding combinatorics explains why the odds are what they are — it doesn't change your actual probability of winning.
- Every single combination, whether it "looks random" or not, has exactly the same 1-in-28,989,675 chance in a 6/55 draw.
- A larger number pool (like 55 versus 52) always means more combinations, and therefore longer jackpot odds — this is simple, unavoidable maths, not a design flaw or advantage.
- No amount of number-selection strategy changes these underlying probabilities, in a 6/55 game or any other lottery format.