Just making sure I have my head on straight when it comes to the whole probability thing.

One card is drawn from a deck of 52. What is the probability that it is:

(a): A diamond?

(b):A King?

(c):An Ace or King?

Working:

(a):There are

or

ways of picking a card, and there are 13 diamond cards so there are

or

ways of picking a diamond. So there the probability of drawing a diamond card is

.

(b):There are

or

ways of picking a card, and there are 4 Kings so there are

or

ways to draw a king. So the probability of drawing a King is

.

(c):There are

or

ways of picking a card, there are 4 Aces and 4 Kings so there are 8 cards to choose from so, there are

or \frac{8!}{1!7!}=8 ways to draw either of the cards.

Therefore, the probability of drawing either an Ace or King is

Am I doing it right?