How many $9-$bit strings $($strings made of $0$ s and $1$ s that are of length $9)$ are there which:

$($a$)$ Start with the sub$-$string $101?$ Briefly explain.

$($b$)$ Have weight $5($i$.$e$.,$ contain exactly five $1$s$)$ and start with the sub$-$string $101?$ Briefly

explain.

$($c$)$ Either start with $101$ or end with $11($or both$)?$ Briefly explain.

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