Feed Me

A note to readers: I now have an RSS feed, accessible on the right toolbar ('Atom'). When used with appropriate software/sites (I have feeds on my homepage at My Yahoo), this will let you know when I've put up a new post--useful for a blog like this, where posts come strictly at random intervals. As always, I encourage feedback, which will bring more-frequent and more closely-tailored posts.

I try not to do throwaway posts, so how can I salvage this one? Hmm... a puzzle suggests itself:

Modern undergraduate that you are, you're watching bootleg 'Scrubs' episodes on your laptop. This goes on for three hours or so. Meanwhile, your site-feeds page occasionally updates to display someone's new blog post. When your favored blogs post, the content hits your feed within 10 minutes, but the precise delay is nondeterministic--could be 0, 10, or anything in between.

You register the order in which the feed updates come in. Now: is there an efficient method to calculate the number of 'true orders' in which the bloggers could have made their updates?

For example: say updates A, B, C came at 12:30, 12:35, and 12:41 respectively. Then this is consistent with the true-orders ABC, BAC, ACB, but not with, e.g. CAB. Thus the answer here is 3 ways.

Good luck! Does your method work if each individual blogger has their own (known) interval of possible delays?

Clarification: I haven't solved this problem. It might be #P-complete, and the proof of this might be very technical. It seems related to work on counting linear extensions of posets (which is #P-complete in general), discussed by Suresh here.