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A club with $x$ members is organized into four committees such that

  1. each member is in exactly two committees, 
  2. any two committees have exactly one member in common.

Then $x$ has

  1. exactly two values both between $4$ and $8$
  2. exactly one value and this lies between $4$ and $8$
  3. exactly two values both between $8$ and $16$
  4. exactly one value and this lies between $8$ and $16$
in Combinatory by Veteran (424k points)
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1 Answer

+1 vote

Answer: $\mathbf B$


This problem can be converted into the graphical form where each nodes represent a committee and the edges represent the member.


So, this problem reduces to nothing but a complete graph. in which each edge can have exactly two nodes(members) or two nodes(members) have exactly one edge(committee).

Hence, $\mathbf B$ is the correct option.

by Boss (12.9k points)
edited by

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