Out of 100 students, two sections of 40 and 60 are formed.

My friend and I are among the 100 students.

Total number of ways of selecting 2 students out of 100 students $={ }^{100} \mathrm{C}_{2}$

(a) 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 $={ }^{40} \mathrm{C}_{2}+{ }^{\infty} \mathrm{C}_{2}$

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

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

(b) P(we enter different sections)

= 1 − P(we enter the same section)

$=1-\frac{17}{33}=\frac{16}{33}$