PROBLEM $5-$ Given a random network of $500$ nodes with average node degree of $10,$ which of the following is likely to be closest to the average path length of the network? Show your work. $($IE$490-10$ points; IE$590-10$ points$)$

a$.2\mathrm{.}5$

b$.1\mathrm{.}5$

c$.2\mathrm{.}0$

d$.2\mathrm{.}25$