A deck of playing cards has four suits, with thirteen cards 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.Which statements are true? Check all that apply.The total possible outcomes can be found using 52C5.The total possible outcomes can be found using 52P5.The probability of choosing two diamonds and three hearts is 0.089.The probability of choosing five spades is roughly 0.05The probability of choosing five clubs is roughly 0.0005.

Answer:Step-by-step explanation:Which statements are true? Check all that apply. The total possible outcomes can be found using 52C5. The total possible outcomes can be found using 52P5. The probability of choosing two diamonds and three hearts is 0.089. The probability of choosing five spades is roughly 0.05 The probability of choosing five clubs is roughly 0.0005.Since it can be chosen in any order, we use combination and not permutation. The number of ways of choosing 5 cards from a group of 52 cards is 52C5.The probability of choosing two diamonds and three hearts = [tex]\frac{^{13}C_2*^{13}C_3}{^{52}C_5} = 0.0086[/tex]  so the third one is not true.The probability of choosing five spades = [tex]\frac{^{13}C_5}{^{52}C_5}[/tex] ≈ 0.0005. The fourth statement is not trueThe probability of choosing five clubs  = [tex]\frac{^{13}C_5}{^{52}C_5}[/tex] ≈ 0.0005, the fifth one is. So the answer is the first and fifth statement.