calculating a game's probabilities.

goneforeign

There's a weekly game at the London Guardian, the blog host poses a topic and the readers respond with pop music titles that fit the topic. Every week there are close to or over 1000 readers responding, many with multiple suggestions, in total there are over 2000 suggestions each week. When the game closes the host selects the 'best' 10 from the 2000. Recently there's been a rash of cases where single individuals have selected 3 of the final 10.
My question is, what is the probability of this happening and what's the probability of it happening 3 weeks out of six [with different readers]?
Or to ask it another way, what are the odds of this happening?