Carter$($they$/$them$)$ plans to go into the Berkshires for the summer for a vacation. They have

one problem: traveling to their final destination is going to be a tricky. They plan to leave

from Boston and end up at Williamstown.

$$ Boston has $3$ trains that go to Pittsfield, $3$ trains that goes to New York City, and $4$

buses that go to New York City.

$$ From New York City, there are $3$ trains that go to Pittsfield and $2$ buses that go to

Williamstown.

$$ From Pittsfield, there are $4$ buses that go to North Adams and $1$ bus that goes to

Williamstown.

$$ From North Adams, there are $3$ buses that go to Williamstown.

How many ways can they get to Williamstown from Boston?