# Odds winning the lottery (with certain conditions)

Hi,

Here's a question i was planning to answer
but too tired to think
or too hard for me to answer
too lazy to research

Here's the question.

Lets say 6/49 lottery.

200pts
a.) whats is the odds of winning the lottery if we remove combinations that contains at least 3 consecutive number combinations?
say
1,2,3, 22,23,25
41,42,43, 12,34,20

300pts
b.) also remove atleast  2(consecutive numbers combinations)
1,2, 44,45, 33,36
2,3, 10,11, 33,32
22,23, 25,26, 5,7

quoting:http://www.math.mcmaster.ca/fred/Lotto/
Jackpot (all six winning numbers selected)
There are a total of 13,983,816 different groups of six numbers which could be drawn from the set {1, 2, ... , 49}. To see this we observe that there are 49 possibilities for the first number drawn, following which there are 48 possibilities for the second number, 47 for the third, 46 for the fourth, 45 for the fifth, and 44 for the sixth. If we multiply the numbers 49 x 48 x 47 x 46 x 45 x 44 we get 10,068,347,520. However, each possible group of six numbers (combination) can be drawn in different ways depending on which number in the group was drawn first, which was drawn second, and so on. There are 6 choices for the first, 5 for the second, 4 for the third, 3 for the fourth, 2 for the fifth, and 1 for the sixth. Multiply these numbers out to arrive at 6 x 5 x 4 x 3 x 2 x 1 = 720. We then need to divide 10,068,347,520 by 720 to arrive at the figure 13,983,816 as the number of different groups of six numbers (different picks). Since all numbers are assumed to be equally likely and since the probability of some number being drawn must be one, it follows that each pick of six numbers has a probability of 1/13,983,816 = 0.00000007151. This is roughly the same probability as obtaining 24 heads in succession when flipping a fair coin!

we have 1/13,983,816 probability of winning 6/49
What are the Odds now?
A)
B)

thank you.
Member_2_4694817

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Member_2_4694817

BTW, a quick for-loop can confirm the theoretical results. I just checked the no-three-in-a-row variant this way because with its many subcases I was afraid I might have lost overview.

shouldnt i get higher probability if i dont bet on "No-2-in-a-row"?

i was expecting a higher probability with B than A. since there should be fewer "No-3-in-a-Row" than "No-2-in-a-row"

im trying to verify b.

i mean - higher probability betting on "No-2-in-a-row" than "No-3-in-a-row".
I've always been curious to opt out the no 3 in a row patterns and see how that turned out.  e.g. 1,2,3 / 1,3,5 / 1,4,7 / etc.
SOLUTION

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