# The face-down deck of cards contains four hearts six diamonds three clubs and six spades. What is the probability that the first two cards drawn will both be spades?

Aug 19, 2016

$\frac{5}{57}$

#### Explanation:

First we need to know how many cards are in the deck. Since we have 4 hearts, 6 diamonds, 3 clubs, and 6 spades, there are $4 + 6 + 3 + 6 = 19$ cards in the deck.

Now, the probability that the first card is a spade is $\frac{6}{19}$, because there are $6$ spades out of a deck of $19$ cards total.

If the first two cards drawn will be spades, then after drawing one spade we will have $5$ left - and since we took a card out of the deck, we will have $18$ cards total. That means the probability of drawing a second spade is $\frac{5}{18}$.

To wrap it up, the probability of drawing a spade first ($\frac{6}{19}$) and second ($\frac{5}{18}$) is the product of these:
$P \left(\text{Drawing two spades}\right) = \frac{6}{19} \cdot \frac{5}{18} = \frac{5}{57}$