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The official site says the chances of winning the jackpot is 1 in 175,711,536, when I do the math, I get a different number. Can someone correct me please

5 balls out of lot of 56 
1 ball out of a lot of 46

Total possible combination:

56 x 55 x 54 x 53 x 52 x 46 = 21,085,384,320

Edit :

I am going to add this

The odds of winning a $2 ticket is listed as 1/75 on the megamillion site. Shouldn't that be 1/46.

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up vote 6 down vote accepted

The difference is that you are counting every possible permutation rather than every possible combination. For instance, the sequence $10,20,30,40,50$ is equivalent to $50,40,30,20,10.$ Since you have $5!$ equivalent permutation for each combination (given there are 5 numbers picked out of the big lot), you need to divide your result by $120$: giving the published odds of $1:175,711,536$.

As for your followup question, I just checked the game's rules and you win that prize iff you have the bonus number and none of the primaries.

The general equation you are looking for is the number of permutations of m balls picked out of n:

$\frac{n!}{(n-m)!}$

Getting none of the primary balls means getting a combination of all the numbers except those you picked (51!/46!) divided by all the possible combinations (56!/51!). So the odds of having none of the primary numbers is (very close to) 61% - the odds of that and having the bonus ball give a bit over 1:75 odds of winning that $2

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Ok i forgot about combinatios vs computation. But the chances of winning $2 is said to be 1/75. Shoudn't that be 1/46. AS the only ball matters is the last ball and chances of that is 1/46. –  TomCat Apr 2 '12 at 0:14
    
It should, I expect, but I'm not familiar with the game's rules so I could not tell you what other factors might be taken into account. For instance, do you win that lot only if you have no other correct ball (which would reduce the odds), or some other factor like this? –  Marc A. Pelletier Apr 2 '12 at 0:21
    
yes if the last ball match, the first 5 does not matter. You win $2. The last ball is picked out of 46 balls. –  TomCat Apr 2 '12 at 1:02
    
@TomCat The others do matter at least a little. For example, if the others are all correct you will win the jackpot rather than $2. –  Alex Becker Apr 2 '12 at 6:11
    
you are going to ge the other numbers in any case. The probability of winning just a 2$ ticket using the megamillion ball should be 1/46 as it picked of a lot of 46 balls. –  TomCat Apr 2 '12 at 12:33
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