\binom{8}{3} = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56

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

# Understanding Binomial Coefficients: A Deep Dive into $\binom{8}{3} = 56$ When exploring the world of combinatorics, few expressions are as fundamental and widely used as the binomial coefficient $\binom{n}{k}$. This mathematically elegant formula counts the number of ways to choose $k$ items from a set of $n$ items without regard to order. Today, we’ll unpack the meaning and calculation of $\binom{8}{3}$, revealing why this number holds key importance in mathematics, statistics, and everyday problem-solving. ## What Is $\binom{8}{3}$? $\binom{8}{3}$ represents the number of combinations of 8 items taken 3 at a time. It answers the question: In how many different ways can 3 items be selected from a group of 8 unique items?