Concepts · 3 min read
Lottery Odds Explained: Combinations Behind Pick-6 Games
Why combinations
The order the balls are drawn does not matter, only which six are chosen — a combination. Compute it with the permutation and combination calculator.
49C6
- 49C6 = 13,983,816
Step-by-step working 3 steps
- 1Order does not matter, no repeats
nCr = n! / (r!(n−r)!) = nPr / r!
Use combinations when you only care which items are chosen (committees, lottery picks).
- 2Compute nPr and r!
49P6 = 10,068,347,520 6! = 720
- 3Divide
10,068,347,520 ÷ 720 = 13,983,816
Different game sizes
| Game | Possible tickets | Chance of jackpot |
|---|---|---|
| 6 of 45 | 8,145,060 | 1 in 8,145,060 |
| 6 of 49 | 13,983,816 | 1 in 13,983,816 |
| 6 of 59 | 45,057,474 | 1 in 45,057,474 |
Partial matches
Matching exactly 5 of 6 in a 6/49 game: choose 5 of the 6 winning numbers (6 ways) and 1 of the 43 others, giving 6 × 43 = 258 tickets, a chance of 0.001845%, about 1 in 54,201.
A sensible takeaway
Because the jackpot odds are so small, lotteries are best treated as entertainment. Buying more tickets raises your chances only in proportion to the tiny base number. Compare with other rare events in the birthday paradox.
Frequently asked questions
Do some numbers come up more often?
In a fair draw every combination is equally likely, including 1-2-3-4-5-6.
How do I calculate other lottery odds?
Use nCr with n = numbers available and r = numbers drawn; add a bonus-ball factor if the rules require it.
Keep reading
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Charts & referencesFactorials Chart: 0! to 20! and What They Count
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