Combinatorics
Our final section regards binomial coefficients. They are part of the mathematical field of combinatorics, but we will introduce them in the context of the binomial distribution, which we will meet multiple times in the book.
Binomial coefficients
Along with the normal or Gaussian distribution, the binomial distribution is one of the most common distributions we will encounter as data scientists. It is the distribution of the number of times, 
, we observe a particular outcome in a set of 
observations, where in each observation there are only two possibilities that can occur. Given we are interested only in the total number, 
, of successful outcomes of a particular type, a large part of calculating the associated probability comes down to calculating how many ways we can distribute or arrange the 
successes between the observations. The answer is given by the binomial coefficient 
. This is defined mathematically as follows:
Eq. 62
Here, 
means 
factorial...
