Instructions

Directions for the following two questions:

Let S be the set of all pairs (i, j) where 1 <= i < j <= n , and n >= 4 (i and j are natural numbers). Any two distinct members of S are called āfriendsā if they have one constituent of the pairs in common and āenemiesā 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.

Question 10

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?

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