Question

Find the binomial coefficient (4 2)

Answer 1

$\large\begin{array}{l} \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot (4-2)!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3 \cdot \diagup\!\!\!\! 2!}{2!\cdot \diagup\!\!\!\! 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3}{2\cdot 1}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{12}{2}}\\\\ \boxed{\begin{array}{c}\mathsf{\dbinom{4}{2}=6}\end{array}}\quad\longleftarrow\quad\textsf{this is the answer.} \end{array}$


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