Certainly, let’s find the probability of drawing 4 aces in 5 cards from a well-shuffled deck.
1. Determine the total number of possible hands:
- We are drawing 5 cards from a deck of 52 cards.
- The total number of possible hands is given by the combination formula:
- 52 choose 5 = 52! / (5! * (52-5)!) = 52! / (5! * 47!) = 2,598,960
2. Determine the number of ways to draw 4 aces:
- There are 4 aces in a deck.
- We need to choose 4 of them: 4 choose 4 = 4! / (4! * (4-4)!) = 1
- We also need to choose 1 card that is not an ace. There are 48 non-ace cards in the deck.
- Number of ways to choose 1 non-ace card: 48 choose 1 = 48! / (1! * (48-1)!) = 48
- Total number of ways to draw 4 aces and 1 non-ace: 1 * 48 = 48
3. Calculate the probability:
- Probability = (Number of ways to draw 4 aces) / (Total number of possible hands)
- Probability = 48 / 2,598,960
- Probability = 1/54,145
Therefore, the probability of drawing 4 aces in 5 cards from a well-shuffled deck is extremely low: 1/54,145