How many $12-$bit strings $($that is$,$ bit strings of length $12)$ are there which:

a$.$ Start with the sub$-$string $101?$

b$.$ Have weight $5($i$.$e$.,$ contain exactly $51$s$)$ and start with the sub$-$string $101?$

c$.$ Start with $101$ or end with $11($or both$)?$

d$.$ Have weight $5$ and start with $101$ or end with $11($or both$)?$