How many $10$

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

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

$128$

Have weight $6($i$.$e$.,$ contain exactly $61$s$)$ and start with the sub$-$string $011?$

$35$

Either start with $011$

or end with $01$

$($or both$)?$

$352$

Have weight $6$ and either start with $011$

or end with $01$

$($or both$)?$