\binom{5}{1} = 5

Fri, 01 May 2026 03:56:36 +0000

Understanding the Binomial Coefficient: Why \(\binom{5}{1} = 5\) Holds Key Significance in Mathematics If you’ve ever explored combinatorics or simple algebra, you’ve likely encountered the binomial coefficient—a fundamental concept that reveals how many ways we can choose items from a larger set. Among its basic but powerful expressions, \(\binom{5}{1} = 5\) stands out as a straightforward example of choice and probability. ### What is \(\binom{5}{1}\)? The binomial coefficient \(\binom{n}{k}\), read as "n choose k," represents the number of ways to choose \(k\) elements from a set of \(n\) distinct elements, without regard to order. It is defined mathematically as: