Compare the fractions 9/25 and 9/24. To four decimal places, 9/25 = 0.3600 and 9/24 = 0.3750. To four decimal places, these numbers are not equivalent.
In a small group: Picking one person and not putting them back changes the math for the next person significantly.
In a big group: Picking one person and not putting them back doesn't really change anything.