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

$0/20$ 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.

can some one write me a python program for this? I got $32$ for a$)$ and $1518$ for b$)$ and that isn't correct. Thank you a lot