On Wed, 11 Feb 2009 00:52:11 -0800 (PST), Archie <email@example.com> wrote:
>Say you can choose six numbers out of 59. What is the probability that >three (and only three) will be consecutive? This is complicated by the >fact that numbers appear in order from least to greatest. What if the >six numbers contain 2 sets of 3 consecutive numbers? > >I'm not finding any easy formula for this. > >Thanks! Do you pick six numbers at random and use the order they are picked in, or do you pick six numbers and then sort them before looking for runs of three? The probabilities are different.
For three consecutive numbers, then they must fall into one of the following patterns:
abcxxx xabcxx xxabcx xxxabc
where abc are three consecutive ascending numbers and the x's are any other numbers. Work out the probabilities for each pattern and sum them.