# In a card game using a standard 52 card deck, 4-card hands are dealt. What's the probability of being dealt 3 diamonds?

##### 1 Answer

#### Explanation:

In a standard deck, there are 13 ordinal cards (Ace - 10, Jack, Queen, King) and in each of 4 suits (Hearts, Diamonds, Clubs, Spades) for a total of

We're asked to find the number of possible 4-card hands containing exactly 3 diamonds. The order of the draw doesn't matter, so we're dealing with a Combinations problem (if the order did matter, it'd be a Permutation problem).

The formula for a Combination is

So what is it that we're picking and picking from?

First, we need to pick 3 diamonds from a selection of 13, so that is:

There are calculators that will do the math for you, like this one but I'll do the math here:

So that's 3 cards down with 1 to go. This last card cannot be a diamond, so we have the remaining suits to pick from. While there are fancy ways to write this, I'll settle for

Now to put this all together. We multiply the two numbers to get the final total of the number of hands possible: