Evaluate Binomial Coefficient

Evaluate the binomial coefficient inom{7}{5}.

In this problem, you are asked to evaluate a specific binomial coefficient, which is a fundamental concept in combinatorics. Binomial coefficients are typically represented using the notation "n choose k" and are used to count the number of ways to choose k items from a set of n items without regard to the order of selection.

This concept is not only central to combinatorics but is also widely applicable in probability, statistics, and various branches of mathematics.

When approaching problems involving binomial coefficients, it's important to recall their relationship to the binomial theorem, which provides a way to expand expressions of the form (a + b)^n. The coefficients in the expansion correspond to the binomial coefficients, indicating their significance in algebraic expressions and polynomial expansions.

Furthermore, understanding Pascal's Triangle can provide intuitive insight into the properties of binomial coefficients, as each coefficient is the sum of the two directly above it in the triangle.

For this specific problem, evaluating inom{7}{5} involves understanding that this is equivalent to calculating the number of combinations of 5 items that can be selected from a total of 7.

Recognizing that inom{n}{k} = inom{n}{n-k} simplifies the computation, as recognizing symmetry reduces it to evaluating inom{7}{2}. This principle of symmetry in binomial coefficients can significantly streamline the process of evaluation.