**Question: **Let S be the set of all pairs (i, j) where, 1≤ i < j ≤ n and n≥ 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’, consider any two members of S that are friends. How many other members of S will be common friends of both these members?

\(\frac{1}{2}\left( {{n^2} - 5n + 8} \right)\) | |

\(2n - 6\) | |

\(\frac{1}{2}n\left( {n - 3} \right)\) | |

\(n - 2\) | |

\(\frac{1}{2}\left( {{n^2} - 7n + 16} \right)\) |

**Show Answer**

## CAT Quant Questions with Video Solutions

CAT Quant Questions Set 01CAT Quant Questions Set 02

CAT Quant Questions Set 03

CAT Quant Questions Set 04

CAT Quant Questions Set 05

CAT Quant Questions Set 06

Back to Main Page

#### CAT Quant Online Course

- 1000+ Practice Problems
- Detailed Theory of Every Topics
- Online Live Sessions for Doubt Clearing
- All Problems with Video Solutions

₹ 2999