From a pack of 52 cards, 4 are drawn one by one without replacement. Find the probability that all are aces.

To find the probability of drawing 4 aces from a standard deck of 52 cards without replacement, we can follow these steps:

Understanding the Total Outcomes

When drawing 4 cards from a deck of 52, the total number of ways to choose any 4 cards is calculated using combinations:

• Total combinations = C(52, 4) = 52! / (4!(52-4)!) = 270725

Calculating Favorable Outcomes

Next, we need to determine how many ways we can draw 4 aces. Since there are only 4 aces in the deck, there is only one way to choose all 4 aces:

• Favorable combinations = C(4, 4) = 1

Finding the Probability

The probability of drawing all 4 aces is given by the ratio of favorable outcomes to total outcomes:

Probability = Favorable outcomes / Total outcomes

Substituting the values we found:

Probability = 1 / 270725

Final Result

The probability of drawing 4 aces from a pack of 52 cards without replacement is 1 in 270725, or approximately 0.0000037.