\binom{16}{4} = \frac{16 \times 15 \times 14 \times 13}{4 \times 3 \times 2 \times 1} = 1820

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

# Understanding \binom{16}{4} and Why 1820 Matters in Combinatorics If you’ve ever wondered how mathematicians count combinations efficiently, \binom{16}{4} is a perfect example that reveals the beauty and utility of binomial coefficients. This commonly encountered expression, calculated as \\(\frac{16 \\ imes 15 \\ imes 14 \\ imes 13}{4 \\ imes 3 \\ imes 2 \\ imes 1} = 1820\\), plays a crucial role in combinatorics, probability, and statistics. In this article, we’ll explore what \binom{16}{4} means, break down its calculation, and highlight why the result—1820—is significant across math and real-world applications. --- ## What Does \binom{16}{4} Represent?