How many $9-$bit strings $($strings made of $0$ s and $1s$ 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.