Peak capacity and statistical resolution probability

The efficiency of a separating system is best demonstrated by its peak capacity. This shows how many components can be separated in theory within a certain k range as peaks of resolution 1. The number of theoretical plates, N, of the column used must be known, as the isocratic peak capacity, n, is proportional to its square root  

A column with 10 000 theoretical plates has a breakthrough time of 1 min. Calculate the number of peaks of resolution 1 that can possibly be separated over a 5 min period. 

The above-mentioned equation for n in fact is only valid for isocratic separations and if the peaks are symmetric the peak capacity is larger with gradient separations. Tailing decreases the peak capacity of a column. In real separations the theoretical plate number is not constant over the full k range. However, it is even more important to realize that a hypothetical parameter is discussed here. It is necessary to deal with peaks that are statistically distributed over the accessible time range. The theory of probabilities allows us to proceed from ideal to near-real separations. Unfortunately, the results are discouraging. 

What is the Probability that a Certain Component of the Sample 

Mixture will be Eluted as a Single Peak and not Overlapped by 

What is the probability that a certain component of the sample mixture will be eluted as a single peak and not overlapped by other components  

P = probability related to a single component m = number of components in the sample mixture 

---