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

[zalook]

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.

 

[zalook]

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