document.write( "Question 1113745: A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the specified type.
\n" ); document.write( "Three of a kind (three of one denomination, one of another denomination, and one of a third)
\n" ); document.write( "For those unfamiliar with playing cards, here is a short description. A standard deck consists of 52 playing cards. Each card is in one of 13 denominations: ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, jack (J), queen (Q), and king (K), and in one of four suits: hearts (), diamonds (), clubs (), and spades (). Thus, for instance, the jack of spades, J, refers to the denomination of jack in the suit of spades.
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Algebra.Com's Answer #728851 by math_helper(2461) $\"\"$ $\"About$

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Choices for the rank (value) of the triple: 13C1
\n" ); document.write( "Choices for the suits of the triple: 4C3 (3 out of 4 suits must be dealt)
\n" ); document.write( "Choices for nonmatching 2 cards: 12C2
\n" ); document.write( "Choices for suits of the nonmatching 2 cards: (4C1)^2\r
\n" ); document.write( "\n" ); document.write( "Total number of three-of-a-kind hands (not categorized as other hands, such as full-house):
\n" ); document.write( "(13C1)(4C3)(12C2)(4C1)^2 = 13*4*66*16 = 54912\r
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\n" ); document.write( "Ans: Total number of possible three-of-a-kind hands is 54912
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