Elements of combinatorial analysis

This is an important distribution that is frequently observed in natural phenomena. We will see later in this book how the Gaussian distribution emerges naturally for many physical phenomena. 

Johann Carl Friedrich Gauss, considered by many the greatest mathematician ever to exist, introduced this distribution in the early nineteenth century, although the normal distribution was first described by Abraham de Moivre in 1733.  

A well-known example of a Gaussian distribution is the celebrated Maxwell-Boltzmann distribution of velocities of gas particles. In one dimension, we write 

We derive this equation and discuss it in detail in Chapter 5. 

A fundamental principle of combinatorial analysis is that if an event Ei can occur in ni ways and an event Ez can occur in nz different ways, then the number of ways both can occur is equal to the product ninz. 

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