Lottery Odds Explained: The Combinations Behind Powerball and Mega Millions
October 21, 2026
Lottery odds come from combinations, because the order in which the balls are drawn does not matter. In Powerball, you choose 5 white balls from 69 and 1 red ball from 26. The number of ways to pick the white balls is C(69,5) = 11,238,513, and multiplying by 26 red-ball choices gives 292,201,338 possible tickets, so a single ticket has a 1 in 292,201,338 chance of winning the jackpot.
Skip the math and get your answer instantly:
Open the Permutation & Combination Calculator →Combinations Step by Step
C(n, k) = n! ÷ (k! × (n − k)!). For 5 balls from 69: 69 × 68 × 67 × 66 × 65 ÷ (5 × 4 × 3 × 2 × 1) = 11,238,513. Using combinations rather than permutations avoids counting the same set of numbers in different orders, as 5! = 120 orderings correspond to each set.
The red ball is drawn separately, so the two results multiply. This is the multiplication principle of counting.
| Game | How numbers are drawn | Total combinations | Jackpot odds |
|---|---|---|---|
| Powerball | 5 of 69, plus 1 of 26 | 292,201,338 | 1 in 292.2 million |
| Mega Millions | 5 of 70, plus 1 of 25 | 302,575,350 | 1 in 302.6 million |
Putting the Odds in Perspective
One in 292 million is hard to grasp. If you bought one ticket in every draw twice a week, you would expect to win the jackpot about once in 2.8 million years. Your chance is roughly the same as flipping a fair coin and getting heads 28 times in a row.
Games and rules change over time, including the number of balls, so check the current format. The odds are the same for every ticket, and common patterns such as birthdays do not improve them, although they can increase the chance that you share a prize with others.
Expected Value
The expected value of a ticket is the sum of each prize times its probability. For most lotteries, it is below the ticket price once you include taxes, the lump-sum discount, and the chance of splitting the jackpot. Treat tickets as entertainment, not an investment, and set a budget you are comfortable losing.
Frequently Asked Questions
How are lottery odds calculated?
By counting the number of possible combinations of numbers. One ticket's chance is 1 divided by that total.
Why combinations and not permutations?
Because the order in which the balls are drawn does not matter for winning.
Do quick picks have better odds?
No. Every ticket has the same chance, whether chosen randomly or by hand.
What are the odds of winning any prize?
They are much better than the jackpot odds, often around 1 in 25 for a Powerball prize of any size, but check the current game rules.