Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that 

(a) you both enter the same section? 

(b) You both enter the different sections?

My friend and I are among the 100 students.

Total number of ways of selecting 2 students out of 100 students = ¹⁰⁰C₂

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

∴ Number of ways in which both of us enter the same section = ⁴⁰C₂ + ⁶⁰C₂

∴ Probability that both of us enter the same section = ^{(40C₂ + 60C₂)}/_¹⁰⁰C2

= ^{(780 + 1770)}/₄₉₅₀ = ²⁵⁵⁰/₄₉₅₀ = ¹⁷/₃₃

(b) P(we enter different sections) = 1 − P(we enter the same section)

= 1 − ¹⁷/₃₃ = ¹⁶/₃₃