( ^75P_2 - ^75C_2 ) = ?

Answer: Option D

$$\begin{array}{rl}& =\left({}^{75}{P}_2-{}^{75}{C}_2\right)\\ & =\left\{\frac{75!}{75!-2!}-\frac{75\times 74}{2}\right\}\\ & =\frac{75!}{73!}-\left(75\times 37\right)\\ & =\frac{75\times 74\times 73!}{73!}-\left(75\times 37\right)\\ & =\left(75\times 74-75\times 37\right)\\ & =75\times 37\times \left(2-1\right)\\ & =\left(75\times 37\right)\\ & =2775\end{array}$$