$6\mathrm{.}3.$b$.$ Counting paths $2$

$\frac{0\mathrm{.}0}{20\mathrm{.}0}$ points $($graded$)$

Consider the network shown in the image. A double headed arrow iharrj indicates

that there is an edge $ij$ and an edge $ji.$

a$)$ Compute the number of paths consisting of exactly $10$ edges, which start at the

vertex $1,$ end at the vertex $2,$ and do not pass through the vertex $3.$

b$)$ Compute the number of paths consisting of exactly $10$ edges, which start at the

vertex $1,$ end at the vertex $2,$ and pass through the vertex $3$ at least once.

plz do part a and b