This paper is about mathematical biology as a new fast growing and cooperative field of the two sciences: biology and mathematics. The challenge is that more quantitative becomes the biology science, wider and deeper becomes the application of mathematics in this science, hence more exciting results will be in the global scope. Many experiments in biology need quantification in order to make measurements, to discover and estimate the influence of different factors in the phenomenon under study, and draw right conclusions. An example is the estimation of the total number of choices a fly faces while travelling through the apparatus for fractionating the flies. The combinations of the successive choices result with a great number. Comparative experiments estimate differences in response between treatments or between the two groups involved in the experiment. There are many cases where the comparisons are biased, no matter how precise the measurements are done, because of the way a group is partitioned into two subgroups. The biologist needs to know all the possible partitions and the respective numbers of comparisons, make them part of the experiment and find out which partition give
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