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