A startup has 6 founders at a strategy retreat. Each pair of founders independently has a one-on-one strategy conversation with probability $1/2$.

Question:
What is the probability that the final conversation network has exactly 4 links?

A. $\frac{1001}{\mathrm{32768}}$ 

B. $\frac{1365}{32768}$

C. $\frac{1820}{32768}$

D. $\frac{3003}{\mathrm{32768}}$

E. $\frac{5005}{32768}$