Consider an urn containing a finite set of values.
An item is selected at random from the urn. Then it is returned
to the urn along with another item with the same value. Next
a value is selected at random from the reconstituted urn
and it and a copy our returned to the urn. This process is
repeated until \(k\) additional items have been added to the
original urn. The original composition of the urn along with the selected
values, in order, are returned.