$(15$ points$)$ Consider a standard deck of $52$ playing cards, which consists of four suits: hearts, diamonds, clubs, and spades, each containing $13$ cards.

$($a$)$ How many ways can a player be dealt a flush in a five$-$card poker hand? A flush consists of five cards all of the same suit.

$($b$)$ How many total five$-$card poker hands are possible from a standard deck of $52$ cards?

$($c$)$ What is the probability of being dealt a flush in a five$-$card poker hand?