My friend and I are among the $100$ students.

Total number of ways of selecting $2$ students out of $100$ students $=^{100} C_{2}$

The two of us will enter the same section if both of us are among $40$ students or among $60$ students.

$\therefore$ Number of ways in which both of us enter the same section $=^{40} C_{2}+^{60} C_{2}$

$\therefore$ Probability that both of us enter the same section

$ = \frac{{^{40}{C_2}{ + ^{60}}{C_2}}}{{^{100}{C_2}}}$ $=\frac{\frac{\lfloor {40}}{\lfloor {2\lfloor {38}}}+\frac{\lfloor {60}}{\lfloor {2\lfloor {58}}}}{\frac{\lfloor {100}}{\lfloor {2\lfloor {98}}}}=$ $\frac{(39 \times 40)+(59 \times 60)}{99 \times 100}=\frac{17}{33}$