Discrete Mathematics
# Combinations

$10$ points are drawn on a plane such that exactly $4$ of the points are collinear and among the remaining points, no three points are collinear. How many distinct lines can be drawn by connecting any $2$ among these $10$ points?

SupposeHow many ways can the integers $1,2,3,4,5,6$ be arranged such that $2$ is adjacent to either 1 or 3?

**Details and assumptions**

2 could be next to both 1 and 3.