document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116827>Question 1116827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different 5-card poker hands contain exactly two kings?\r<BR>\n" );
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document.write( "I tried C(13,5) x C(4,2) x C(11,3) but I kept getting the wrong answer.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731760 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 52 cards in the deck.\r<BR>\n" );
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document.write( "you draw a hand.\r<BR>\n" );
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document.write( "that's 5 cards total.\r<BR>\n" );
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document.write( "there are 4 kings in the deck.<BR>\n" );
document.write( "there are 48 other cards in the deck.\r<BR>\n" );
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document.write( "the number of ways you can get 2 kings is c(4,2) = 6<BR>\n" );
document.write( "the number of ways you can get 3 other cards is (c(48,3) = 17296.\r<BR>\n" );
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document.write( "the total number of ways you can get 5 cards where 2 are kings and 3 are something else is 6 * 17296 = 103776.\r<BR>\n" );
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document.write( "to see how this works, try something a lot simpler.\r<BR>\n" );
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document.write( "assume the deck has 4 kings and 1 jack and a queen only.\r<BR>\n" );
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document.write( "that's a total of 6 cards.\r<BR>\n" );
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document.write( "how many ways can you get a 3 card hand that has 2 kings plus 1 other card.\r<BR>\n" );
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document.write( "if we're correct, the number of ways should be c(4,2) * c(2,1) = 12.\r<BR>\n" );
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document.write( "let's see if that's true.\r<BR>\n" );
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document.write( "let the kings be the letters a,b,c,d.<BR>\n" );
document.write( "let the queen be the number 1.<BR>\n" );
document.write( "let the jack be the number 2.\r<BR>\n" );
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document.write( "you are drawing 3 cards from the deck of 6.\r<BR>\n" );
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document.write( "the number of ways you can get 2 kings that are diferent from each other is c(4,2) = 6\r<BR>\n" );
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document.write( "that would be:\r<BR>\n" );
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document.write( "a,b<BR>\n" );
document.write( "a,c<BR>\n" );
document.write( "a,d<BR>\n" );
document.write( "b,c<BR>\n" );
document.write( "b,d<BR>\n" );
document.write( "c,d\r<BR>\n" );
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document.write( "for each one of these pairs of kings, you can draw either a queen or a jack.\r<BR>\n" );
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document.write( "if a queen, you would get:\r<BR>\n" );
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document.write( "a,b,1<BR>\n" );
document.write( "a,c,1<BR>\n" );
document.write( "a,d,1<BR>\n" );
document.write( "b,c,1<BR>\n" );
document.write( "b,d,1<BR>\n" );
document.write( "c,d,1\r<BR>\n" );
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document.write( "if a jack, you would get:\r<BR>\n" );
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document.write( "a,b,2<BR>\n" );
document.write( "a,c,2<BR>\n" );
document.write( "a,d,2<BR>\n" );
document.write( "b,c,2<BR>\n" );
document.write( "b,d,2<BR>\n" );
document.write( "c,d,2\r<BR>\n" );
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document.write( "that'a  total of 12 possible ways.\r<BR>\n" );
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document.write( "the method of solution appears to be good with a simple example.\r<BR>\n" );
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document.write( "i would try itthe same method with the more complex example and see if it's right.\r<BR>\n" );
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document.write( "if not, let me know what the solution is supposed to be and i'll try to see what other method might work.\r<BR>\n" );
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document.write( "my solution using this method is c(4,2) * c(48,3) = 103776.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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