combin(31,7)

combin(31,7)=?

$$\small{
\begin{array}{rcl}
\dbinom{31}{7} &=&
\dfrac{31}{7}
\cdot \left( \dfrac{30}{6} \right)
\cdot \left( \dfrac{29}{5} \right)
\cdot \left( \dfrac{28}{4} \right)
\cdot \left( \dfrac{27}{3} \right)
\cdot \left( \dfrac{26}{2} \right)
\cdot \left( \dfrac{25}{1} \right)\\\\
\dbinom{31}{7} &=&
\dfrac{31}{7}
\cdot 5
\cdot \left( \dfrac{29}{5} \right)
\cdot 7
\cdot 9
\cdot 13
\cdot 25 \\\\
\dbinom{31}{7} &=&
31
\cdot 29
\cdot 9
\cdot 13
\cdot 25 \\\\
\mathbf{\dbinom{31}{7}} & \mathbf{=} & \mathbf{2~629~575}
\end{array}
}$$

C(31,7) = 2,629,575