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Definition D2167
Binomial coefficient

Let $n, m \in \mathbb{N}$ each be a D996: Natural number.
The binomial coefficient with respect to $(n, m)$ is the D996: Natural number $$\binom{n}{m} : = |\mathcal{P}_m \{ 1, \ldots, n \}|$$

Let $n, m \in \mathbb{N}$ each be a D996: Natural number.
The binomial coefficient with respect to $(n, m)$ is the D996: Natural number $$\binom{n}{m} : = \# \left\{ E \subseteq \{ 1, \ldots, n \} : |E| = m \right\}$$
Children
 ▶ D4197: Central binomial coefficient
Results
 ▶ R3611 ▶ R5670 ▶ R2786: Complement property of binomial coefficient ▶ R2787: Pascal's rule ▶ R1831: Real arithmetic expression for binomial coefficient ▶ R4945: Real binomial theorem for exponent five ▶ R4944: Real binomial theorem for exponent four ▶ R5172: Real binomial theorem for exponent seven ▶ R5171: Real binomial theorem for exponent six ▶ R4943: Real binomial theorem for exponent three ▶ R3090: Scaling property of binomial coefficient
Conjectures
 ▶ C15: Singmaster's conjecture