Card Probability Problems

#1
Scenario: If you have a standard deck of 52 cards and you draw 2 of those cards without replacement, what is the probability of:

1) P(getting a King and an Ace)

a) If the cards were drawn sequentially, I believe the answer is P(Getting a King then an Ace) + P(Getting an Ace then a King) which should be:

(4/52)(4/51)+(4/52)(4/51)

b) If the cards were drawn simultaneously, I believe the answer is:

(4C1)(4C1)/(52C2)

2) P(Getting a King and a Hearts)

This is difficult for me because I don't know how to account for the possibilities that the King drawn is a King of Hearts and/or the Hearts drawn is a King. So here are my guesses:

a) If the cards were drawn sequentially, I believe the answer should be
P(Getting a non-Hearts King then a non-King Hearts) + P(Getting a non-King Hearts then a non-Hearts King) + P(Getting a King of Hearts then a Hearts) + P(King of Hearts then a King) + P(Getting a non-Hearts King then a King of Hearts) + P(Getting a non-King Hearts then a King of Hearts), which should be:

(3/52)(12/51)+ (12/52)(3/51) + (1/52)(12/51) +(1/52)(3/51) + (3/52)(1/51) + (12/52)(1/51)

b) If the cards were drawn simultaneously, I believe the answer should be:

[(3C1)(12C1) + (1C1)(12C1) + (1C1)(3C1)] / (52C2)


Any help with this would be appreciated!
Thanks.
 
#2
Part 1 is right. Both answers are the same.
Part 2 is trickier. One way is to do it in two parts. First find the probability of the KH and any other card with a pack of 52 cards.
Then remove the KH and start with a pack of 51 cards, 3 kings and 12 hearts and apply the same reasoning as for part 1.