Mock AMC 8 #1 - Problem 11

There are 25 students in a classroom, each one assigned a number from 1 to 25, inclusive. If every even numbered student shakes hands once with every other even numbered students, and every odd numbered student shakes hands once with every other odd numbered students, how many total handshakes were exchanged?

(\textbf{A})\;144\quad(\textbf{B})\;313\quad(\textbf{C})\;288\quad(\textbf{D})\;128\quad(\textbf{E})\;250

Enter your answer as a capital letter.