How many combinations are there in the lottery?

If you’ve ever thought about playing the lottery, there is probably one question in the front of your mind. . . what are my chances of winning?

article body image

You may also wonder if different lottery combinations have equal chances of winning and how to choose the best lottery numbers. The truth is that there’s really no best kept secret on how to win the lottery or increase your chances of winning. 

Playing the lottery is all about the luck of the draw. However, your chance of winning can vary depending on a number of factors. Understanding lottery games and combinations is a step in the right direction toward cracking the code on how to win the lottery. 

Keep reading to learn more about common questions surrounding UK lottery numbers and lottery combinations.

article body image

So, how many combinations are there?

With so many lottery formats, the precise number of possible lottery combinations will depend on which lottery you choose to play. Naturally, lotteries in which the player has to choose fewer numbers from a smaller pool will have fewer total lottery combinations available to choose from. That’s not to say that there aren't still plenty of lottery combinations to choose from, even if the required number of choices or the numbers you can select from are relatively low. 

To figure out just how many lottery combinations are possible for each individual lottery, you can use the following formula.

  1. Take the total number of choices that are available.

            Example: Choose numbers between 1-10. 

  1. Pick a different number for each selection that you are required to make. 

           Example: Select four numbers. 

  1. Account for the fact that for your first choice, you will have 10 numbers to select from. For your second choice, you will have 9 remaining selections. For the third number, you will have 8 choices. Finally, for the fourth number, you will have 7 remaining numbers to choose from. Multiply those choices together. 

           Example: 10 x 9 x 8 x 7=5,040 

  1. Consider that the order of these numbers, essentially, does not matter. As a result, we need to divide by all of the ways to arrange the selected numbers.

           Example: 4 x 3 x 2 x 1 = 24 (since we selected 4 numbers)

  1. Finally, we take the total number of possible choices and divide by the number of ways to arrange these numbers. 

           Example: 5,040 ÷ 24 = 210. Therefore, in this hypothetical scenario, there would be 210 different ways to                 pick four numbers from 1-10 or 210 different lottery combinations. 

Keep in mind that most popular lotteries will have many more available combinations, as it is commonly required to pick more choices from a larger range of numbers. This is merely an example to showcase how to calculate the possibilities for different lotteries - highlighting just how slim your odds may be.

article body image

How many lottery combinations are there in Euromillions?

Euromillions is an exceptionally popular lottery for UK residents. This is, in part, due to its ease of play. Players can “set it and forget it,” choosing their numbers and waiting for a notification of any winnings. 

For many players though, watching the winning numbers getting drawn live is all part of the thrill. Players can watch live, check the web/their app, or scan their ticket in store to see if they have won. 

Aside from its convenience, the Euromillions can also attribute its popularity to the life-changing jackpots. Players have an opportunity to win big. The largest recorded Euromillions win was in December 2023, when a single lucky player scooped over £200,000,000!

The Euromillions transnational lottery requires seven matching numbers to win the jackpot.  These seven numbers consist of 5 main numbers (from 50) and 2 Lucky Star Numbers (from 12). Using this information, and the formula above, there are 139,838,160 Euromillions combinations. While this number is staggering, many players still feel like it is worth a shot at £2.50 per ticket. 

Can you buy every combination of lottery ticket?

Theoretically, yes, one could buy every combination of lottery ticket. Realistically, not so much. 

article body image

Let’s take what we know about the Euromillions lottery for example. With 139,838,160 Euromillions combinations costing £2.50 per ticket, that would cost £349,595,400. While there are few who may have that kind of money to spend, even if the jackpot is hit, they may still not make any profit. Especially if any jackpot has to be split with additional winners, buying that many lottery tickets would be an incredible feat with little chance for significant (or any) profit. 

Has anyone ever bought every lottery combination?

Just because it’s not practical, doesn’t mean nobody has ever tried. In 1992, a group attempted to game the Virginia state (US) lottery by purchasing all 7 million possible lottery combinations - but only successfully bought 2.4million lottery combinations before they ran out of time. The logistics of actually purchasing enough lottery tickets to cover every combination is just, well, not very logical. 

article body image

How many combinations are there in the National Lottery?

The National Lottery is undoubtedly host to one of the UK’s most popular lottery games - Lotto. Similar to Euromillions, players can test their luck with random computer-selected numbers or choose their own. Draws are held on Wednesdays and Saturdays. Players can play one week at a time or select up to four weeks to play their selected numbers. 

The National Lottery’s popular Lotto game requires a sequence of six numbers from 1-59. The National Lottery trumps even the Euromillions lottery with a whopping 45,057,474 possible lottery combinations. 

article body image

How many combinations are there with 6 numbers in the lottery?

That would depend on the range of numbers from which players have to choose from. For example, six numbers chosen from 1-10 would produce far fewer lottery combinations than a game in which numbers could be chosen from 1-50. For a more specific answer, refer to the mathematical formula above.

Are all lottery combinations equally likely?

Yes, technically, all lottery combinations are equally likely to be winners. However, some sequences of numbers may be more popular - resulting in a shared jackpot and ultimately, less money. 

For example, unoriginal sequences such as 1,2,3,4,5,6 could be used more and therefore yield less winnings than a lottery combination that only one person has chosen. For this reason, players may want to avoid number combinations in sequences, numbers that occur in songs, or may be popular for any other reason. Since birthdays are commonly used to select lottery numbers it is often the case that numbers above 31 share jackpots less when they feature on winning tickets...

article body image

There you have it. There is no secret, cheat code, or magic number. That is what makes the lottery fun for all players! With thousands - and even millions - of lottery combinations to choose from, the odds of hitting the jackpot are not very high. 

However, understanding the statistics behind each lottery game can give you the power of knowing just how big, or small, those odds are. And if you happen to want a direct comparison of the odds of winning Euromillions, Lotto, Thunderball, Set For Life and all of The Health Lottery's lottery games you can find that here. Spoiler alert, you may want to play The Big Win, All or Nothing or QuickWin once you see how the odds stack up...

For players who care less about the maths and more about the thrill of the game,  it helps to know that proceeds from all major lottery tickets go towards a good cause.

article body image

The current society benefitting from funds raised is EWM Health CIC T/A HL West Midlands

The Health Lottery operates on behalf of 6 Community Interest Companies (CICs), managing 6 society lotteries that operate in 12 geographical regions across Great Britain. These exist to help tackle health inequalities in their respective areas. People’s Health Trust (PHT) is an independent charity that assesses grant applications and award funding across the 12 regions. Read about some of the good causes HERE. For information regarding all funded projects or to submit a grant application visit PHT HERE. 20.34% of every lottery draw ticket and online scratchcard purchased is donated to good causes. 36.02% is spent on prizes. 43.64% is spent expenses (actual expenses exceed this figure). Our average annual proceeds from lotteries are £12.5m. The odds of winning The Big Win jackpot are (1 in 2.1m) and the odds of winning any Big Win prize is (1 in 9.7). The odds of winning the All or Nothing jackpot is (1 in 1.35m) and the odds of winning any All or Nothing prize is (1 in 4.5). The odds of winning a QuickWin jackpot is (1 in 2.1m) and the odds of winning any QuickWin prize is (1 in 6). All winning lottery numbers are selected using an approved random number generator (RNG). Click on the links below for full T&Cs and FAQs for each of our games.

Please help us to support vital health causes in your community. Each of the 6 society lotteries is licensed by the Gambling Commission.