document.write( "Question 918735: Determine how many 5-card poker hands there are with: \r
\n" ); document.write( "\n" ); document.write( "a) A full house of kings over 7's (3 kings and 2 7's) \r
\n" ); document.write( "\n" ); document.write( "b) 3 of a kind if the fourth and fifth cards must be different \n" ); document.write( "

Algebra.Com's Answer #557411 by Edwin McCravy(20055) $\"\"$ $\"About$

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Determine how many 5-card poker hands there are with:

a) A full house of kings over 7's (3 kings and 2 7's)

Choose the 3 kings C(4,3) = 4 ways.\r\n" );
document.write( "Choose the 2 7's C(4,2) = 6 ways.\r\n" );
document.write( "That's C(4,3)C(4,2) = (4)(6) = 24 ways.

b) 3 of a king if the fourth and fifth cards must be different.

Choose the 3 kings C(4,3) = 4 ways.\r\n" );
document.write( "Choose the ranks of the two non-king cards in C(12,2)=66 ways, since\r\n" );
document.write( "there are 12 non-king ranks.\r\n" );
document.write( "Choose the suit of the higher ranking non-king card in 4 ways.\r\n" );
document.write( "Choose the suit of the lower ranking non-king card also in 4 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's C(4,3)C(12,2)(4)(4) = (4)(66)(4)(4) = 4224 ways. \r\n" );
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document.write( "Edwin

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