Originally Posted by

**wik_chick88** suppose that a large number of people standing in a queue are asked to reorder themselves so that they line up in order of height. what is the approximate probability that at least one person is in the same position after the reordering as they were before?

i did up lists for up to 4 people and the results are:

1 person, Pr = 1 = 1

2 people, Pr = 1/2 = 0.5

3 people, Pr = 2/3 = 0.667

4 people, Pr = 5/8 = 0.625

i cannot for the life of me see a pattern, considering the 2 people probability means that the probabilities aren't even in decreasing order. i have done that particular probability correct, right?

also, the question has a hint:

∞

ex = S __x__r

r=0 r!

WHAT DOES THIS HAVE TO DO WITH THE QUESTION?!?!