How many $11-$bit strings $($that is$,$ bit strings of length $11)$ are there which:

a$.$ Start with the sub$-$string $011?$

b$.$ Have weight $4($i$.$e$.,$ contain exactly $41\text{'}$s$)$ and start with the sub$-$string $011?$

c$.$ Either start with $011$ or end with $01($or both$)?$

d$.$ Have weight $4$ and either start with $011$ or end with $01($or both$)?$