How many combinations are there in the lottery?
How many combinations are there in the lottery?
292,201,338 for Powerball
The lifetime odds of being struck by lightning in the United States are roughly 1 in 15,000. You are about 20,000 times more likely to be struck by lightning than to win a Powerball jackpot with one ticket.
A US Powerball ticket picks 5 numbers from 69 and one more from 26, giving C(69,5) × 26 = 11,238,513 × 26 = 292,201,338 combinations. The UK National Lottery, 6 from 59, has 45,057,474. EuroMillions has 139,838,160. These are exact, which makes the odds statements unusually honest by the standards of gambling — the difficulty is that people are poor at feeling the difference between one in a million and one in three hundred million.
How the figure is arrived at
The combinations formula C(n,k) = n! / (k!(n-k)!), because the five main numbers are unordered, multiplied by the independent choice of the extra ball. Buying every combination has occasionally been attempted and is defeated by logistics and by the risk of splitting the jackpot, not by the arithmetic.
Other numbers and possibilities counts
- How many combinations does a Rubik's Cube have? 43,252,003,274,489,856,000 — about 43 quintillion
- How many ways can you shuffle a deck of cards? about 8 × 10^67
- How many possible chess games are there? about 10^120 games; about 4.8 × 10^44 legal positions
- How many digits of pi have been calculated? about 202 trillion
- How many possible passwords are there? 6.6 quadrillion for eight characters — 540 sextillion for twelve
- How many Sudoku puzzles are there? 6,670,903,752,021,072,936,960 completed grids
- How many prime numbers are there under a million? exactly 78,498
- How many possible positions are there in Go? about 2.08 × 10^170
Common questions
- How many combinations are there in the lottery?
- 292,201,338 for Powerball
- How is that estimated?
- The combinations formula C(n,k) = n! / (k!(n-k)!), because the five main numbers are unordered, multiplied by the independent choice of the extra ball. Buying every combination has occasionally been attempted and is defeated by logistics and by the risk of splitting the jackpot, not by the arithmetic.
Related pages
- How many combinations does a Rubik's Cube have? 43,252,003,274,489,856,000 — about 43 quintillion
- How many ways can you shuffle a deck of cards? about 8 × 10^67
- How many possible chess games are there? about 10^120 games; about 4.8 × 10^44 legal positions
- How many digits of pi have been calculated? about 202 trillion
- How many possible passwords are there? 6.6 quadrillion for eight characters — 540 sextillion for twelve
- How many Sudoku puzzles are there? 6,670,903,752,021,072,936,960 completed grids
- How many prime numbers are there under a million? exactly 78,498
- How many possible positions are there in Go? about 2.08 × 10^170
- How many people are there in the world? Living things and the natural world
- How many stars are there in the universe? Space and the universe
- How many countries are there in the world? Things people built
- How many bones are in the human body? The human body
- How many grains of sand are there on Earth? Living things and the natural world
- How many ants are there in the world? Living things and the natural world
Sources
- Calculated on this page — At One Place