document.write( "Question 698962: Consider a standard deck of 52 cards. How many 5-card hands can be formed that includes:\r
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Algebra.Com's Answer #431147 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
a)all diamonds
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document.write( "That's 13 diamonds, Choose 5.  That's C(13,5) = 1287\r\n" );
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document.write( "Choose the face cards. That's 12 face cards, Choose 3. That's C(12,3)\r\n" );
document.write( "For each of those choices of the 3 face cards, we\r\n" );
document.write( "choose the non-face cards. That's 40 non-face cards, Choose 2.\r\n" );
document.write( "That's C(40,2).\r\n" );
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document.write( "Answer: C(12,3)×C(40,2) = 220×780 = 171,600. \r\n" );
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\n" ); document.write( " c) at most 2 Queens
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document.write( "There are three cases. No queens, 1 queen, and 2 queens\r\n" );
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document.write( "1.  No queens.  That's 48 non-queens, Choose 5. That's C(48,5)=1,712,304.\r\n" );
document.write( "2.  1 queen. That's 4 queens, choose 1.  That's C(4,1)=4. \r\n" );
document.write( "For each of those choices of the 1 queen, we choose the 4 non-queens. \r\n" );
document.write( "That's 48 non-queens, Choose 4.  That's C(48,4). So for case 2, the answer\r\n" );
document.write( "is C(4,1)×C(48,4) = 4×194580 = 778,320\r\n" );
document.write( "3. 2 queens. That's 4 queens, choose 2.  That's C(4,2)=6. \r\n" );
document.write( "For each of those choices of the 2 queens, we choose the 3 non-queens. \r\n" );
document.write( "That's 48 non-queens, Choose 3.  That's C(48,3). So for case 3, the answer\r\n" );
document.write( "is C(4,2)×C(48,3) = 6×17296 = 103,776.  \r\n" );
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document.write( "Total = 1,712,304 + 778,320 + 103,776 = 2,594,400\r\n" );
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document.write( "We choose the two denominations of the pairs.  \r\n" );
document.write( "That's 13 denominations Choose 2, or C(13,2).\r\n" );
document.write( "We choose the suits for the lower pair.  That's 4 suits Choose 2, or C(4,2).\r\n" );
document.write( "We choose the suits for the higher pair.  That's 4 suits Choose 2, or C(4,2).\r\n" );
document.write( "We choose the 5th card that doesn't have the same denomination as either\r\n" );
document.write( "of the two pair. (We must be sure we don't have a full house!)\r\n" );
document.write( "That's 11 denominations that the pairs aren't of, choose 1.  That's C(11,1).\r\n" );
document.write( "We choose the suit of the 5th card.  That's 4 suits choose 1.  That's C(4,1).\r\n" );
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document.write( "Answer: C(13,2)×C(4,2)×C(4,2)×C(11,1)×C(4,1) = 78×6×6×11×4 = 123,552.\r\n" );
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document.write( "Edwin
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