How many five-card hands (drawn from a standard 52-card deck) contain a three-of-a-kind?

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

Three-of-a-kind: this hand has the pattern AAABC where A, B, and C are from distinct kinds. The number of such hands is,

¹³C₁ * ⁴C₃ * ¹²C₂ * ⁴C₁ * ⁴C₁

= 13 * 4 * 66 * 4 * 4

= 54912

Therefore, five-card hands contain a three-of-a-kind by 54912 ways

Answer 2

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