A deck of playing cards has four suits, with thirteen cards Which statements are true? Check all that apply. in each suit consisting of the numbers 2 through 10, a jack, a queen, a king, and an ace. The four suits are hearts, diamonds, spades, and clubs. A hand of five cards will be chosen at random. The total possible outcomes can be found using \( { }_{52} \mathrm{C}_{5} \). The total possible outcomes can be found using \( { }_{52} \mathrm{P}_{5} \). The probability of choosing two diamonds and three hearts is 0.089 . The probability of choosing five spades is roughly 0.05

Let’s delve into the world of cards! First off, when calculating the total possible combinations of a five-card hand from a standard deck of 52 playing cards, we indeed use combinations (denoted as \( { }_{52} \mathrm{C}_{5} \)), because the order of the cards doesn’t matter in a poker hand or similar games. So, that statement is true! Now, talking about the probabilities, it’s a fun little math game! The probability of specific combinations of cards, like drawing two diamonds and three hearts, is calculated using combinatorial methods. Hence, if that value is stated as 0.089, go ahead and check your calculations! Similarly, the rough estimation of drawing five spades being 0.05 sounds plausible, but make sure to double-check the math. Probabilities like these can take you on a wild statistical ride!