Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. 

# of ways to choose 2 aces and another card: 4*3/2 times 48=288

# of total ways to choose 3 cards: 52*51*50/(3*2*1)=22100
answer is 228/22100 or 72/5525

To find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards, we need to consider the number of favorable outcomes (hands with two aces) and the total number of possible outcomes (all three-card hands).

First, let's determine the number of favorable outcomes:

There are four aces in a deck, and we need to choose two of them. This can be done in (4 choose 2) ways, denoted as C(4, 2) or (4C2).

C(4, 2) = (4!)/((2!)*(4-2)!) = (4*3)/(2*1) = 6.

Now, let's determine the total number of possible outcomes:

We are choosing three cards from a deck of 52 cards, so this can be done in (52 choose 3) ways, denoted as C(52, 3) or (52C3).

C(52, 3) = (52!)/((3!)*(52-3)!) = (52*51*50)/(3*2*1) = 22100.

Finally, let's calculate the probability:

Probability = (Number of favorable outcomes)/(Total number of possible outcomes)

Probability = C(4, 2)/C(52, 3) = 6/22100.

Therefore, the probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 6/22100.

To find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards, we'll need to calculate the number of favorable outcomes (drawing two aces) and divide it by the total number of possible outcomes (drawing any three cards).

First, let's determine the number of ways to choose two aces from the four available in the deck. We can do this using the combination formula, denoted by "nCr".

The number of ways to choose two aces from four is calculated as:
4C2 = 4! / (2!(4-2)!) = 6

Next, we'll determine the number of ways to choose any three cards from the 52 available in the deck. This is also calculated using the combination formula:

The number of ways to choose three cards from 52 is calculated as:
52C3 = 52! / (3!(52-3)!) = 22,100

To find the probability, we'll divide the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 6 / 22,100

Thus, the probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 6/22,100.