Suppose that there are 6 people in a room. Show that one can always find a group of 3 people such that either nobody in the group knows anybody in the group or everybody in the group knows everyone in the group. (b) Show that this conclusion does not hold if there are only 5 people in the room.

Suppose that there are 6 people in a room. Show that one can always find a group of 3 people such that either nobody in the group knows anybody in the group or everybody in the group knows everyone in the group. (b) Show that this conclusion does not hold if there are only 5 people in the room.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

(a) Suppose that there are 6 people in a room. Show that one can always find a group of 3 people such that either nobody in the group knows anybody in the group or everybody in the group knows everyone in the group.
(b) Show that this conclusion does not hold if there are only 5 people in the room.

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