**Let S be the set of all pairs (i, j) where 1 ≤ i ≤ j < n and n ≥ 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) and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies.**

**Q1) For general n, how many enemies will each member of S have?**

**(1) n – 3**

(2) 1/2 (n^{2} – 3n – 2)

(3) 2n – 7

(4) 1/2 (n^{2} – 5n + 6)

(5) 1/2 (n^{2} – 7n + 14)

**Q2) For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members?**

**(1) 1/2 (n**^{2}- 5n + 8)

(2) 2n – 6

(3) 1/2 *n (n – 3)

(4) n – 2

(5) 1/2 (n^{2}– 7n + 16) (CAT 2007)