document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=520629>Question 520629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of (a) four hearts and one spade? (b) three red cards and two black cards? (c) at least 3 face cards? (d) 2 aces and 2 face cards? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #346155 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=346155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. <BR>\n" );
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document.write( "How many different hands are there consisting of <BR>\n" );
document.write( "(a) four hearts and one spade?<BR>\n" );
document.write( "# of ways to get 4 hearts: 13C4 = 715<BR>\n" );
document.write( "# of ways to get 1 spade: 13C1 = 13<BR>\n" );
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document.write( "Total # of ways = 715*13 = 9295<BR>\n" );
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document.write( "(b) three red cards and two black cards? <BR>\n" );
document.write( "# of ways to get 3 red = 26C3 = 2600 <BR>\n" );
document.write( "# of ways to get 2 black = 26C2 = 325<BR>\n" );
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document.write( "Total # of ways = 845,000<BR>\n" );
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document.write( "(c) at least 3 face cards?<BR>\n" );
document.write( "There are 12 face cards:<BR>\n" );
document.write( "3 face cards: 12C3*40C2 = 220*780 <BR>\n" );
document.write( "+ 4 face cards:  12C4*40C1 = 495*40 <BR>\n" );
document.write( "+ 5 face cards: 12C5*40C0 = 792*1<BR>\n" );
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document.write( "Total # =  171600 + 19800 + 792 = 192,192<BR>\n" );
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document.write( "(d) 2 aces and 2 face cards?<BR>\n" );
document.write( "# of ways to get 2 aces: 4C2 = 6<BR>\n" );
document.write( "# of ways to get 2 face cards: 12C2 = 66<BR>\n" );
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document.write( "Total # of ways = 6*66 = 396<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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