I guess I didn't realize that might not be the case for all classes of problems. I don't have any formal coursework in the subject.haruspex said:It depends whether order matters. In the present case, it makes no difference whether you pick a winner, then a loser, or the other way around. So for k selections, the factor k! appears in the denominator for both the number of successful combinations and the total number of combinations.
In a random walk with an absorbing barrier the order does matter. If one step away from the barrier, what is the probability of reaching it in three goes (with 50:50 at each step)?
You only need two of the three in the right direction: an evens chance.
But if the first step is in the right direction it doesn’t matter about the other two: so 5/8.