Well firstly I would just like to say, that I don't only want to work out the probability, I also want to make some exceptions. We will use a typical lottery, 6 numbers are drawn from a range of 49 and if the 6 numbers on a ticket match the numbers drawn, the ticket holder is a jackpot winner.
I understand that the numbers 1,2,3,4,5,6 have the same probablility as any other six numbers. BUT! I want to exclude all consecutive numbers so I would like to calculate the probability of winning the lottery, but I don't want to take into account any consecutive numbers. For example:
1, 13, 23, 45, 46, 7
I know that this sounds stupid, but I just want to exclude them.
This is how far I've got... (Skip red if you know)
Starting with a bag of 49 differently-numbered lottery balls, there is clearly a 1 in 49 chance of predicting the number of the first ball selected from the bag. When the second number is picked there are now only 48 balls so there is a 1 in 48 chance and so on.
49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520
Next the order in which the numbers are selected doesn't matter, so...
1 x 2 x 3 x 4 x 5 x 6 = 720
10,068,347,520 / 720 = 13,983,816
So there is a 1 in 13,983,816 chance of winning?
Ok now this is the bit I am struggling with! How do I now ignore any set that has 2 or more consecutive numbers? Any help would be great, it's just something I am interested. I guess it's the fact that my mind is telling me that consecutive numbers isn't going to happen frequently, and It'll make my chances look mor elikely if I ignore them, and will make me think I'm going to win. 5% of my winnings to the first person to help