Question 183
How many ways of lining up $2010$ white stones and $2010$ black stones along a horizontal straight line are there so as to satisfy the following condition?
* In the line-up there are odd number of pairs consisting of one white stone and one black stone with the white one lying on the right of the black one.
* In the line-up there are odd number of pairs consisting of one white stone and one black stone with the white one lying on the right of the black one.