How many $10-$bit strings $($that is$,$ bit strings of length $10)$ are there which:

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

$$

b$.$ Have weight $7($i$.$e$.,$ contain exactly $71\text{'}$s$)$ and start with the sub$-$string $011?$

$$

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

$$

d$.$ Have weight $7$ and either start with $011$ or end with $01($or both$)?$

$$

Next itemZ