Bosons's amplitude to go into the same state at low temperatures

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Hi I was reading Feynman's third book and I don't understand why, with bosons at low temperatures, 'there's more amplitude to go into the same state than into an unoccupied state by the famous factor √n, where n is the occupancy of the lowest state'.

Thanks.
 
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Since the context could be useful, it's in page 21-8 of the third volume.
 

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