Better off dead

There is a mob of 3000 people, 1 of whom is a zombie while the other 2999 are not.

Every minute, all 3000 people form 1000 groups of three.
If there are any zombies in a group of three, all three end up zombies.

What is the probability that after 5 minutes there will be exactly 100 zombies in the mob?

Please provide up to 5 decimal places as necessary.


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