$$\left( {{}^{75}{P_2} - {}^{75}{C_2}} \right) = ?$$

Solution (By Examveda Team)

$$\eqalign{ & = \left( {{}^{75}{P_2} - {}^{75}{C_2}} \right) \cr & = \left\{ {\frac{{75!}}{{75! - 2!}} - \frac{{75 \times 74}}{2}} \right\} \cr & = \frac{{75!}}{{73!}} - \left( {75 \times 37} \right) \cr & = \frac{{75 \times 74 \times 73!}}{{73!}} - \left( {75 \times 37} \right) \cr & = \left( {75 \times 74 - 75 \times 37} \right) \cr & = 75 \times 37 \times \left( {2 - 1} \right) \cr & = \left( {75 \times 37} \right) \cr & = 2775 \cr} $$