In the game of poker, five cards from a standard deck of 52 cards are dealt to each player.
Assume there are four players and the cards are dealt five at a time around the table until all four players have received five cards.
a. What is the probability of the first player receiving a royal flush (the ace, king, queen, jack, and 10 of the same suit).
b. What is the probability of the second player receiving a royal flush?
c. If the cards are dealt one at a time to each player in turn, what is the probability of the first player receiving a royal flush?
I know that the probability of a royal flush is $\dfrac{1}{649740}$, because of ${_{52}}C_5=2598960$, and $\dfrac{4}{2598960} = \dfrac{1}{649740}$.
But I am struggling to understand how to determine the probability of the first player getting it, etc...
Any help would be greatly appreciated.