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# Maths question

• Registered Users Posts: 625

Ok, I know this is the chess section but hopefully someone can answer my question or a Mod can move this to the appropriate thread.

So the question is about the lotto.

We were talkin about the new "All or nothing" Lotto draw where there are 24numbers to pick from, and you pick any 12 numbers. The idea is to either get 12numbers, or get 0 numbers - both being the jackpot.

Someone said that this is harder to win than the ordinary lotto which has (correct me if im wrong) 46 numbers and you have to get 6 numbers.

So the chances of rinning the lotto jackpot is 46 x 45 x 44 x 43 x 42 x 41 (is this correct ?

so can anybody clear up for me which draw is harder to win...

Thanks !

• The probability of winning the Lotto is 1/(45*44*43*42*41*41/6*5*4*3*2*1) while the all or nothing is 2/(24*23*22*21*20*19*18*17*16*15*14*13/12*11*10*9*8*7*6*5*4*3*2*1) which is a few orders of magnitude less likely according to Excel, which I think is wrong, no calculator handy. But there's the numbers anyway if you feel like working it out.

I know the lotto is a little worse than 8million-1 to win, I'm getting 1.4trillion-1 for all or nothing which I admit feels a little long. :pac:.

Also here would've been a better place for this thread.
http://boards.ie/vbulletin/forumdisplay.php?f=380

• amacachi wrote: »
The probability of winning the Lotto is 1/(45*44*43*42*41*41/6*5*4*3*2*1) while the all or nothing is 2/(24*23*22*21*20*19*18*17*16*15*14*13/12*11*10*9*8*7*6*5*4*3*2*1) which is a few orders of magnitude less likely according to Excel, which I think is wrong, no calculator handy. But there's the numbers anyway if you feel like working it out.

I know the lotto is a little worse than 8million-1 to win, I'm getting 1.4trillion-1 for all or nothing which I admit feels a little long. :pac:.

You need to put brackets around your denominator, the 12!. That's why you're getting 1.4 trillion to one. The ordinary lotto is (45C6)/2, while the all-or-nothing is (24C12)/2. There's no need to type out 24*23*22... You can use a function excel has called combin.

The answers are 4072530 and 1352078, respectively, so the odds on winning the all-or-nothing jackpot are 3 times more likely.

• Why is the ordinary lotto 45C6 /2 and not 45C6?

• komodosp wrote: »
Why is the ordinary lotto 45C6 /2 and not 45C6?

You have to buy at least 2 panels.

P.S. I'm making a fairly basic assumption that they are going to be two different combos.

P.S.S. With the all-or-nothing, you can buy one panel.

• its a one in 1.35 million chance of winning

2 times (12!/24P12)

simply as