The Problem With Buying Every Mega Million Ticket
The #MegaMillions prize is OVER one billion dollars for Tuesday night – so would it make sense to buy every ticket combination? Let’s figure it out!
To calculate the cost of buying every possible $2 ticket combination for Mega Millions with a $1 billion prize, we need to know the total number of unique ticket combinations.
So let’s do the math!
Here’s what we know: The Mega Millions game involves selecting 5 numbers from a pool of 1 to 70 and 1 Mega Ball number from a pool of 1 to 25. To find the number of unique combinations, we can use the formula for combinations:
Number of combinations = C(n, k) = n! / (k! * (n – k)!)
For Mega Millions: n = 70 (the pool of numbers to choose from) k = 5 (the number of numbers to choose)
Number of combinations for 5 numbers = C(70, 5) = 70! / (5! * (70 – 5)!) = 12,103,014
For the Mega Ball number: n = 25 (the pool of numbers to choose from) k = 1 (the number of numbers to choose)
Number of combinations for the Mega Ball = C(25, 1) = 25! / (1! * (25 – 1)!) = 25
Now, to find the total number of unique ticket combinations for Mega Millions, we multiply the two values:
Total number of unique ticket combinations = 12,103,014 * 25 = 302,575,350
Finally, to calculate the cost of buying every possible ticket, we multiply the total number of unique combinations by the ticket price ($2 in this case):
Cost = 302,575,350 * $2 = $605,150,700
So, it would cost approximately $605,150,700 to buy every possible $2 ticket combination for Mega Millions with a $1 billion prize. Still seems like a good deal, right? Wrong. Here’s why:
|
lump sum
$527,900,000 |
|---|---|
|
Cash: $527,900,000 |
|
– $126,696,000 |
|
– $68,589,955 |
|
|
|
|
$332,614,045 |
Take that $332 million and incorporate your state taxes (anywhere from 4.25 percent to 9) and you’re closer to $300,000, 000 (and that’s ONLY if one person wins). As you can see – it’s a bad investment.
But lets just say you go full Elon Musk and decide “what the hell, I still want to do it” and decide to buy 300,000 Mega Millions tickets…how how many people it would take to fill out 300,000 Mega Millions tickets in 24 hours?
(Photo Illustration by Scott Olson/Getty Images)
To calculate the number of people needed to fill out 302,575,350 Mega Millions tickets in 24 hours, we first need to know how long it takes for one person to fill out a single ticket.
Assuming it takes an average of 1 minute for one person to fill out one Mega Millions ticket, we can calculate the number of people required to complete all the tickets in 24 hours (1 day).
Number of people needed = Total number of tickets / Tickets filled per person per day Number of people needed = 302,575,350 / (24 hours * 60 minutes)
Let’s calculate:
Number of people needed = 302,575,350 / (24 * 60) Number of people needed ≈ 210,267.6
Since we can’t have a fraction of a person, we’ll round up to the nearest whole number. Therefore, approximately 210,268 people would be needed to fill out 302,575,350 Mega Millions tickets in 24 hours, assuming each person takes 1 minute to fill out one ticket on average
So not exactly the best idea – but fun to think about! (my head hurts from all this math).
