I'm having trouble figuring out the problem below. I've laid out my approach and it seems combinatorics formulas might help solve this. If anyone can point to me to the right direction i would greatly appreciate it. Not looking for a direct answer, just a path I can follow.
PROVE that In any group of $n \ge 1$ people, there exists a committee with the following two properties:
(a) No $2$ members of the committee are friends and
(b) Every person not included in the committee is a friend of at least $1$ member of the committee.
$n = 10$
$c$ – Committee size
$n-c$ -> every person not included in the committee
each committee member has $c-1$ enemies
$n-c$ people have at least $1$ friend who is a member of $c$