1 $}$ In mathematics, the binomial coefficient is written as ${n \choose k}$ and can be pronounced as “n choose k.” Alternatively, binomial coefficients are also sometimes given the notation C(n, k). In this case, the C stands for the word “choices” or “combination” (Benjamin, 2009, p. 8). This is because there are ${n \choose k}$ ways of choosing k elements from a set containing a number of n elements. For example, we can consider the set A = {1, 2, 3, 4}. If we wish to know how many subsets of 2 can be created using this set, we are essentially asking how many ways there are of choosing 2 elements from a set with 4 total elements. Therefore, we can identify that k = 2 and n = 4. Hence, we have ${4 \choose 2}$. To calculate such a problem, we typically would want to write out by hand all the possible combinations. Doing so, one would find that there are six pairs of size two subsets, namely {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, and {3, 4}. However, it becomes clear to see that when we are dealing with large sets of values, this work can become tedious. Therefore, it is convenient to utilize the following formula: \[{n \choose k} = {(n-k)! \cdot k!} \]