Compute the area covered by cards randomly put on a table

Question

This is an interview question, the interview has been done.

Given a deck of rectangular cards, put them randomly on a rectangular table whose size is much larger than t

Answer 1

Suppose there are n cards of unit area. Let T be the area of the table. For the discretised problem, the expected area covered will be

$ T(1-({{T-1}\over{T}})^n) $