posted on Jun, 8 2010 @ 04:30 PM
As i was saying (UK Lotto):
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!
Good luck punters!