Probability of 17 doing somthing at the same time

Hi there,

A variable number of people are sitting down with a button in front of
them. They all press the button once within a 30 second time frame.

What I need to work out is how many people it would take for the
probability of at least 17 people pressing the button on the same second to
reach 0.1%.

Any help would be much apreciated,
John
.