\binom{7}{2} \times \binom{9}{2} = \left(\frac{7 \times 6}{2 \times 1}\right) \times \left(\frac{9 \times 8}{2 \times 1}\right) = 21 \times 36 = 756

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

Understanding the Combinatorial Equation: \(\binom{7}{2} \ imes \binom{9}{2} = 756\) Factorials and combinations are fundamental tools in combinatorics and probability, helping us count arrangements and selections efficiently. One intriguing identity involves computing the product of two binomial coefficients and demonstrating its numerical value: \[
\binom{7}{2} \ imes \binom{9}{2} = \left(\frac{7 \ imes 6}{2 \ imes 1}\right) \ imes \left(\frac{9 \ imes 8}{2 \ imes 1}\right) = 21 \ imes 36 = 756
\] This article explores the meaning of this equation, how it’s derived, and why it matters in mathematics and real-world applications.