# What is the probability of drawing two cards from a deck and getting an ace and a spade?

Not sure whether to use combinations, permutations, multiplication rule, or fundamental counting rule or what here so this is much appreciated!

### 1 Answer

- δοτζοLv 76 years agoFavorite Answer
There are a few ways to count this, but the easiest is to consider cases. There are 2 cases to consider: 1) Ace of spades is drawn, 2) ace of spades isn't drawn.

If you draw the ace of spades then that one card satisfies the condition and so the second card doesn't matter at all. This is equivalent of drawing any of the other 51 cards and so there's 51 ways of doing this. If you don't draw the ace of spades, then you need one of the 12 spades which isn't an ace and one of the other 3 aces. There are 18 ways to do that (12*3/2). You have to divide by 2 to compensate for the order imposed by doing 12*3. Add these up to give a total of 69 pairs which satisfy the condition and divide by the number of total possible pairs (52 C 2) for a total of about 5.2% probability.