Final answer:
The probability of picking 4 aces in a 5-card hand from a standard deck of cards is about 1/221, corresponding to option D.
Step-by-step explanation:
The probability of picking 4 aces in a 5-card hand from a standard deck of cards is calculated using combinations. First, determine the number of ways to choose 4 aces from the 4 aces available in the deck. This is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose.
For the aces, C(4, 4) = 4! / (4!0!) = 1. Then, we have to pick 1 card from the remaining 48 non-ace cards, C(48, 1) = 48. Multiply these two combinations to get the number ways to choose 4 aces plus another card: 1 * 48 = 48 ways.
Now, we calculate the total number of possible 5-card hands from a 52-card deck, which is C(52, 5) = 52! / (5!(52-5)!) = 2,598,960. Finally, we divide the number of ways to pick 4 aces and another card by the total number of 5-card combinations.
Probability = 48 / 2,598,960 = 1 / 54,145, or approximately 1/221 when simplified. Thus, the correct answer is D) 1/221.