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CAT-2007-Previous Years Paper

Question
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Let S be the set of all pairs (Ij) 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.


For general n, how many enemies will each members of S have?



A 2n – 7

B

C

D n – 3

E

Ans. B

A member (a, b) will have an enemy of the form (c, d) where c, d, a, b are all distinct. Therefore c and d can be chosen in ways.

So, number of enemies

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