answer:The total number of ways to draw 5 cards from a 52-card deck is calculated using combinations: 52 choose 5, which equals 2,598,960. To draw 5 cards of the same suit, we first choose one of the four suits, then choose 5 cards from that suit's 13 cards. This gives us 4 (suits) multiplied by 13 choose 5 (combinations within the suit). 13 choose 5 equals 1,287, so the total number of ways to draw 5 cards of the same suit is 4 x 1,287 = 5,148. The probability of drawing 5 cards of the same suit is the number of favorable outcomes (5,148) divided by the total number of possible outcomes (2,598,960). This equals approximately 0.00198 or 0.198%.

answer:A royal flush is the highest possible hand in many card games, consisting of the ace, king, queen, jack, and ten, all of the same suit. Since there are 4 suits, there are only 4 possible royal flush combinations. In comparison, we previously calculated that there are 5,148 ways to draw 5 cards of the same suit. The probability of drawing a royal flush is 4 (favorable outcomes) divided by 2,598,960 (total possible outcomes), which equals approximately 0.00000154 or 0.000154%. Since 0.198% (5 cards of the same suit) is significantly greater than 0.000154% (royal flush), it is much more likely to draw 5 cards of the same suit than a royal flush.

answer:A straight flush is a hand that contains five cards of sequential rank, all of the same suit. For example, 3-4-5-6-7 of hearts or 10-J-Q-K-A of diamonds. To calculate the number of possible straight flushes, we'll consider two cases. In the first case, the straight flush can start with any card from Ace to 9, giving us 9 possibilities per suit. Since there are 4 suits, this gives us 9 x 4 = 36 possible straight flushes. In the second case, the straight flush starts with a 10, resulting in the highest possible straight flush (10-J-Q-K-A), which is a royal flush. We've already counted the royal flushes (4), so we'll exclude them from this count. However, in a standard definition of a straight flush, the royal flush is a special case of a straight flush. Therefore, the total number of straight flushes is 36 (non-royal) + 4 (royal) = 40. The probability of drawing a straight flush is 40 (favorable outcomes) divided by 2,598,960 (total possible outcomes), which equals approximately 0.0000154 or 0.00154%. Note that this is much lower than the probability of drawing 5 cards of the same suit (0.198%), but higher than the probability of drawing a royal flush (0.000154%).

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