Half-a-Billion-DOLLARS ! ! !

Just went to the "Official" website.
Apparently you must pick 5 out 56 and 1 out of 46.
So.....

56 x 55 x 54 x 53 x 52 X 46 = 2,108,538,472

FINAL Answer !!

If any "Probability & Odds" math genius would care to confirm please feel free.

P.S. And most of us think it's hard to hit a "Roya Flush" ... mere child's play...comparatively.

You have the math wrong your numbers would be if you had to have the numbers in order that they are drawn but you do not. It is like getting a Royal Flush the order does not matter. Here is the math.

56/5 x 55/4 X 54/3 X 53/2 X 52/1 X 46 = 175,771,536.

If you buy one ticket the odds are higher that you will die before the drawing then that you will win! WOW!

The "order" is of no significance.

If you draw 1 ball from the original 56 then there is only 55 "other" numbers it can be paired with.
At that point it is 1 x55 combinations. (It doesn't matter which ball is drawn)
However, "going in" there are 56 choices that can be paired with 55 remaining and after that number is picked there are only 54 "other combinations, etc. etc. etc.

For instance. if you draw the # 7 on the first pick... you dont get 4 MORE choices to pick it again. There are only 55 numbers with which it can be paired, and so on and so on.

You cannot use a "dividing" factorial because you might pick it later. Once it is drawn, it's history.

For example (to make it simple) Use the numbers 1 thru 6 and pick (draw) five of them. What are your odds?
According to your theory it would be: 6/5 x 5/4 x 4/3 x 3/2 x 2/1 = 720/120 = 6/1

Do you REALLY think you could pull the "correct" numbers out once every six times ???

And let's assume I am wrong ... then every person / corporation that can dredge up $ 175 million is (according to your math) $500 + million richer. What a deal !!! And oh shit....what if 10 people do it....then their guaranteed win just became a $125 million dollar LOSS.

Derbycity123's math is correct, . . .but not particularly educational.

The calculation of lottery odds is derived from the study of combinations and permutations. The solution for any lottery is as follows:
The odds of winning, . . . i.e. correctly choosing r-balls out of a total of n-balls is: [n! / (n- r)! X r!)]. The symbol "!" represents the "factorial function" in the formula. The factorial function means multiply the subject digit by each digit below it down to 1; example 5! = 5 X 4 X 3 X 2 X 1 = 120.

So for mega Millions:
[n! / (n-r)! X r!)] = [56! / (56-5)! X 5!] = 56! / 51! X5! =

56 X 55 X 54 X 53 X 52 X 51 X 50 X 49 . . . . X 2 X 1/( 51 X 50 X 49 X . . . . . X 2 X 1) X 5 X 4 X 3 X 2 X 1=

(after canceling out factors) 56 X 55 X 54 X 53 X 52/5 X 4 X 3 X 2 x 1 = 458,377,920 / 120 = 3,819,816

The Mega Ball is selected from 46 balls so it simply multiplies the "5 of 56 choice" above:
3,819,816 X 46 = 175,711,536.


The above formula represents the fact that "the order doesn't matter". This means, f'rinstance that if one has selected the number 7, the number 7 need not be drawn on the first pick, it may be drawn first or second or third or fourth or fifth.
There are 120 ways that the selected 5 numbers could be chosen in different orders.

So 56 X 55 X 54 X 53 X 52 = 458,377,920 if they have to be drawn in order.
Divide by 120, . . . 458,377,920 / 120 = 3,819816
Multiply by 46 Mega ball possibilities, . . . 3,819,816 X 46 = 175,711,536

It's just like the difference between a quinella and an exacta in horse racing.

For those who wish to approach the selection of the Mega Millions numbers scientifically here's the distribution tables for all the drawings since June 2005:





Now one's decisions reduce to, f'rinstance, does one select MegaBall #36 because it has been drawn most often or, . . . does one select MegaBall #28 because it is due.

ok, so what's the difference in payout if you just pick the 5 numbers vs.
the 5 number PLUS the megamillion ball option?????

Cost $1 for just the 5 numbers
Cost $2 for the 5 number pick, plus the megamillion ball number.

You are not accounting for the cash option which reduces the payout well below $500,000,000 and Federal Income taxes which will take away 35%.

I showed earlier what the payback would be if a single entitiy purchased all of the 175,711,536 combinations and was the only winner....$119,397,501.6. If there are two winners that goes to $2,592,501.6. If there are three winners that becomes a $55,911,536 loss.

Here's another interesting chart provided by someone calling himself Durango Bill online:



It looks like, once they sell about 120-million tickets, the odds of at least one winner are about 50-50.

At about 200-million ticket sales there's about a 70% chance of someone winning, . . . just under 40% chance of a single winner and 30% chance of multiple winners.

Just beyond 240-million ticket sales there's a 75% chance of a winner, . . .40% chance of multiple winners and 35% chance of a single winner.

At a bit over 280-milion ticket sales, odds are better than 50% there'll be multiple winners.

DonDiego doesn't know how many they've sold so far, . . . but newspapers across the country report Mega Millions Fever gripping the nation.

Oh, . . . they've raised the estimated annuity jackpot to $540,000,000 (cash option $389,000,000) today; they expect to raise it again tomorrow.

One may purchase a ticket until 10:45pm EDT on 30 March 2012.

There was a group from Australia that purchased 5 million tickets and wound up winning by themselves. Don't remember the exact payout, but it was well worth the investment.

DonDiego is unsure what kiddo1125 is asking, . . .

It costs $1 to play Mega Millions. That's it, . . . $1 to play. The player must select, or have the computer select 5 numbers and a mega-number. For $1.

One cannot just play for the first 5 numbers.

Some States, . . . Mega Million States, . . . permit a player to multiply winnings of non-jackpot prizes by playing for $2. kiddo1125 can click on her state on the cited page to find her State's rules.

The payouts are shown here: How to Play. If one correctly selects the 5 numbers without the Mega Ball the prize is $250,000, . . . except everything is different in California.