The binomial coefficient is a function that allows you to solve basic problems
in combinatorics. The coefficient indicates in how many different ways you can
select k distinct elements from a set of n elements.
The binomial coefficient is determined by the two different numbers n and k
and is usually given by
Binomial(n, k) = n! / (k! * (n-k)!),
where exclamation mark stands for the mathematical factorial. Alternatively, the binomial coefficient can be calculated using Pascal's triangle: By constructing a triangle of the form
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
...
where each number is given by the sum of the two numbers above it (the edges
are filled with 1's), the binomial coefficient of n over k is simply given
by the k'th entry of the n'th row.