Thoughts On Pascal’s Triangle And Corporate Elections

In 1654, two giants of mathematics, Blaise Pascal and Pierre de Fermat, began to exchange letters about games of chance. This correspondence resulted in Pascal writing Traité du triangle arithmétique, avec quelques autres petits traitez sur la mesme matière. This thin book, which was published posthumously, describes a triangular array of numbers and how the triangle may be used in probability problems. The triangle itself was not new, but it became known as Pascal’s Triangle.

Below is a truncated illustration of Pascal’s Triangle. It’s easy to construct the triangle and much harder to explain it. Each number is the sum of the two numbers to the left and right above it. In the second row, for example, 2 is the sum of 1 and 1 above it (the row numbers begin with zero). You can actually keep going ad infinitum.

One of the neat features of Pascal’s Triangle is that it allows you to determine the number possible combinations. This got me thinking about how to use Pascal’s Triangle in the field of corporate law. Suppose we have 10 nominees for election to a 5 person board. What is the possible number of combinations of directors that can be elected? It would actually be pretty tedious to figure this out (as will be seen momentarily).

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