Question

Given n objects arranged in a row, a subset of these objects is called unfriendly if no two of its elements are consecutive. Show that the number of unfriendly subsets each having k elements is

Answer 1

Complete question is;

Given n objects are arranged in a row. A subset of these objects is called unfriendly, if no two of its elements are consecutive. Show that the number of unfriendly subsets of a k-element set is ( n−k+1 )

( k )

Answer:

I've been able to prove that the number of unfriendly subsets of a k-element set is;

( n−k+1 )

( k )

Explanation:

I've attached the proof that the number of unfriendly subsets of a k-element set is;

( n−k+1 )

( k )