$5.$ a$)$ How many bit strings of length $6$ do not have consecutive $1\text{'}$s and end in $0.$ Show tree based counting work. I need tree diagram not any string or any code thing.

root

$/\backslash$

$01$

$/\backslash /\backslash$

$1001$

something like this

b$)$ One wants to go from Detroit to Chicago to Minneapolis to Fargo and may use plane, bus or car with the following conditions. The same mode of transportation cannot be used consecutively, Chicago to Minneapolis cannot use plane, and Minneapolis to Fargo cannot use car. How many travel plans are possible. Show tree based counting work. I need tree diagram not any string or any code thing.

root

$/\backslash$

$01$

$/\backslash /\backslash$

$1001$

for this instead of $0$ and $1$ you can use city name and for the path you can just use initial of transportation.