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AssignmentMultiple Select

Probability with Combinations and Permutations

Question 1 • Fall 24 GMS Geometry: Concepts and Connections B

Which statements are true? Check all that apply.

Answer
A
The total possible outcomes can be found using 52C5.
B
The total possible outcomes can be found using 52P5.
C
The probability of choosing two diamonds and three hearts is 0.089.
D
The probability of choosing five spades is roughly 0.05
E
The probability of choosing five clubs is roughly 0.0005.

Explanation

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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