Question

If three cards are randomly selected in a deck of 52 cards, what is the probability of selecting the ace of clubs, the ace of hearts, and the ace of diamonds in any order?

Options:
a) 1/18,424
b) 1/22,100
c) 1/13,975
d) 1/16,215

Answer 1

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 1/22,100. Option (B) is correct.

Step-by-step explanation:

To find the probability of selecting the ace of clubs, the ace of hearts, and the ace of diamonds in any order, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

There are 52 cards in a deck, and we need to select 3 specific cards. The number of ways to choose these cards is given by the combination formula: C(52, 3) = 52! / (3! * (52-3)!).

Next, we need to determine the number of ways these 3 cards can be arranged. Since the order does not matter, we can use the permutation formula: P(3, 3) = 3! / (3-3)!

Finally, the probability is given by the formula: P = favorable outcomes / total outcomes. Therefore, the probability of selecting the ace of clubs, the ace of hearts, and the ace of diamonds in any order is 1 / 22,100.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.