Evaluate the given binomial coefficient 11 8

Key Concepts

Binomial Coefficient

A binomial coefficient, denoted as C(n, k) or 'n choose k', represents the number of ways to choose k elements from a set of n elements without regard to the order of selection. It is calculated using the formula C(n, k) = n! / (k!(n-k)!), where '!' denotes factorial, the product of all positive integers up to that number.

Factorial

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are fundamental in combinatorics, particularly in calculating binomial coefficients, as they provide the necessary counts of arrangements.

Combinatorial Interpretation

The combinatorial interpretation of binomial coefficients provides a way to understand their significance in counting problems. For instance, C(n, k) counts the number of distinct groups of k items that can be formed from n items, which is essential in probability and statistics for determining outcomes in various scenarios.