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

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

(a) Each member is in exactly two committees

(b) Any two committees have exactly one person in common.

Then $x$ has

(1) exactly two values both between $4$ and $8$

(2) exactly one value that lies between $4$ and $8$

(3) exactly two values both between $8$ and $16$

(4) exactly one value that lies between $8$ and $16$ .

Which one/one of this options are correct ?

I ran out of all ideas . Help needed . Complete solution will be highly appreciated .

• There are $\frac {4 \times 3}{2}=6$ , right ? – Suman Kundu May 8 '17 at 15:03
consider a complete graph on four points $K_4$ and what the edges and vertices represent here.