Question 3 • Fall 24 GMS Geometry: Concepts and Connections B
A five-card hand is unordered, so the total number of possible hands is 52C5; 52P5 would count different orders of the same hand. The probability of five clubs is 13C5 ÷ 52C5 = 1,287 ÷ 2,598,960 ≈ 0.0005, so that statement is true. Two diamonds and three hearts has probability (13C2 × 13C3) ÷ 52C5 ≈ 0.0086, not 0.089. Five spades has the same probability as five clubs, about 0.0005, not 0.05.
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