Each particle has two possibilities: either it is on the left hand side or it is on the right hand side.
The probability of having them equally split is
P(100,100) = 200C100 / 2^200
where 200C100 is the binomial coefficient.
For the uneven distribution we have
P= 2 * 200C160 / 2^200
where the factor 2 comes in because we could have 160/40 or 40/160 as a division.
So the ratio of probabilities is
200C100 /(2 * 200C160 )
= 2.2 * 10^16
Hope this helps!
