Question

Let S be the set of all pairs (i,j) where 1$\le$ i < j $\le$ n and n$\ge$ 4. Any two distinct members of S are called friends, if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n=4, then S={(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}. Here (1,2), (1,3) are friends but (1,4), (2,3) are enemies.
For a general 'n', how many enemies will each member of S have?

• A. $\frac{n^2-3n-2}{2}$
• B. $2n-7$
• C. $\frac{n^2-5n+6}{2}$
• D. $\frac{n^2-7n+14}{2}$

Answer 1

The correct option is C $\frac{n^2-5n+6}{2}$

Option (C) is the correct answer. Check the video for the approach.