IIMB 2001 (QA) PYQs

Consider all six-digit numbers $y_{1} y_{2} y_{3} y_{4} y_{5} y_{6}$ where $0<y_{1}<y_{2}<y_{3}<y_{4}<y_{5}<y_{6}$. If these numbers are arranged in increasing order, what is the sum of the digits in the $72$ nd number in this sequence?

In a sports club, there are 14 male members and 9 female members. A new team of five members needs to be chosen for an upcoming competition, ensuring that there are at least 3 males in the team. Calculate the total number of ways this team can be formed.

There are nine points in a plane such that no three are collinear. Find the number of triangles that can be formed using three points as vertices?