Final answer:
The probability of selecting the ace of clubs, the ace of hearts, and the ace of diamonds in any order from a deck of 52 cards without replacement is 1/5525.
Step-by-step explanation:
The subject is Mathematics, and the grade level is High School. To find the probability of selecting the ace of clubs, the ace of hearts, and the ace of diamonds in any order from a well-shuffled deck of 52 cards without replacement, you need to calculate the probability of drawing each one after the other.
For the first card, the probability of drawing one of the aces is 3/52 since there are 3 aces that you want out of 52 cards. Once you have one ace, there are now 51 cards left. The probability of drawing the second ace now is 2/51. Finally, with two aces gone, there are 50 cards left, and the probability of drawing the third ace is 1/50.
To find the total probability of all three events occurring in sequence, you multiply the probabilities together:
Probability = (3/52) * (2/51) * (1/50)
Which simplifies to:
Probability = 1/5525
Hence, the probability of selecting the ace of clubs, the ace of hearts, and the ace of diamonds in any order from a deck of 52 cards is 1/5525.