Mega Millions is a multistate U.S. lottery in which players choose 5 numbers from 1 to 70 and 1 Mega Ball number from 1 to 25. The total number of possible combinations is 302,575,350, meaning there are that many unique ways to fill out a standard play slip. This figure comes from combining the ways to select the 5 main numbers (C(70,5) = 17,259,390) with the 25 possible Mega Ball choices (17,259,390 × 25 = 302,575,350). The huge pool is the reason jackpot odds are fixed at 1 in 302,575,350 regardless of ticket sales or rollovers.
How the 302,575,350 Figure Is Calculated
The total combinations derive from two independent selection pools: the 5 numbers drawn from a set of 70, and the 1 Mega Ball drawn from a set of 25. Because order does not matter in the main draw, we use combinations (binomial coefficient). The math breaks down as follows: calculate C(70,5) to find main-number combinations, then multiply by 25 for the Mega Ball. This captures every possible permutation of number plus Mega Ball, yielding the headline 302,575,350 unique plays.
Binomial Coefficient Basics
A binomial coefficient C(n,k), read as “n choose k,” counts subsets of size k from a set of n items without regard to order. It is computed as n! / (k! × (n − k)!). For Mega Millions main numbers, this means 70! / (5! × 65!), which simplifies to 12,103,014 / 7, or 17,259,390 distinct main-number groups. Multiplying by 25 Mega Ball options gives 302,575,350 overall combinations.
Step-by-Step Computation
1) Compute C(70,5) = 17,259,390. 2) Multiply by 25 (Mega Ball choices). 3) Result: 302,575,350. Because each draw is independent and the pool sizes are fixed, this total remains constant across drawings. Players sometimes assume fewer combinations due to patterns or quick picks, but every play covers exactly one of these 302,575,350 possibilities.
What 302,575,350 Means for Your Odds
Because there are 302,575,350 distinct tickets, the odds of matching all numbers in a single draw are 1 in 302,575,350. Buying more tickets linearly increases your odds proportionally; 30 tickets give 30 chances out of the same pool, or 1 in 10,085,845 on average. Understanding the denominator helps contextualize claims about odds per prize tier, since each tier corresponds to matching a specific subset of numbers plus the Mega Ball.
Prize Tiers and Matching Rules
Mega Millions prizes are awarded for matching combinations of main numbers plus the Mega Ball. The jackpot requires matching all 5 numbers plus the Mega Ball (1 in 302,575,350). Lower-tier prizes match fewer numbers, with or without the Mega Ball, and each tier has a fixed probability based on how many draws satisfy that condition.
| Matched | Mega Ball | Prize Name | Approximate Odds |
|---|---|---|---|
| 5 | ✓ | Jackpot | 1 in 302,575,350 |
| 5 | ✗ | Match 5 | 1 in 12,607,306 |
| 4 | ✓ | Match 4 + Mega | 1 in 931,022 |
| 4 | ✗ | Match 4 | 1 in 38,793 |
| 3 | ✓ | Match 3 + Mega | 1 in 14,547 |
| 3 | ✗ | Match 3 | 1 in 606 |
| 2 | ✓ | Match 2 + Mega | 1 in 701 |
| 1 | ✓ | Match 1 + Mega | 1 in 89 |
| 0 | ✓ | Mega Ball only | 1 in 12 |
Common Misconceptions About the Combinations
Some players think certain number combinations are less likely, but because draws are random and each number ball is equally probable, all 302,575,350 combinations share the same odds. Quick picks and manually chosen numbers have no mathematical difference in probability. Patterns, birthdays, or frequently drawn numbers do not reduce or increase the chance of any specific combination appearing in a given draw.
How Play Styles Interact With the Combination Count
Whether you choose quick picks or mark your own numbers, you are selecting 1 of the 302,575,350 possible plays. Multiple-entry strategies do not create new combinations; they simply purchase more distinct plays, each consuming one additional chance. Systematic methods like wheeling select multiple combinations explicitly to cover more number groupings, but they do not alter the fundamental 1 in 302,575,350 odds for any single ticket line.