document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191644>Question 1191644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A game uses the 10, jack, queen, king, and ace of hearts and spades. How many 6-card hands contain<BR>\n" );
document.write( "a) an equal number of hearts and spades? <BR>\n" );
document.write( "b) more hearts than spades? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823570 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The total number of ways of choosing 6 of the 10 cards is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2810%2C6%29=210 ALIGN=MIDDLE  ALT=\"C%2810%2C6%29=210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The number of ways of choosing 3 of the 5 cards in each suit is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C3%29%2AC%285%2C3%29=10%2A10=100 ALIGN=MIDDLE  ALT=\"C%285%2C3%29%2AC%285%2C3%29=10%2A10=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER part a: 100<br><BR>\n" );
document.write( "By symmetry, the number of ways of getting more hearts than spades is equal to the number of ways of getting more spades than hearts.  So the number of ways of getting more hearts than spades is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28210-100%29+=+55 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28210-100%29+=+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "ANSWER part b: 55<br><BR>\n" );
document.write( "Note we can find the answer to part b with more straightforward methods.<br><BR>\n" );
document.write( "4 hearts and 2 spades: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C4%29%2AC%285%2C2%29=5%2A10=50 ALIGN=MIDDLE  ALT=\"C%285%2C4%29%2AC%285%2C2%29=5%2A10=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5 hearts and 1 spade: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C5%29%2AC%285%2C1%29+=+1%2A5=5 ALIGN=MIDDLE  ALT=\"C%285%2C5%29%2AC%285%2C1%29+=+1%2A5=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "More hearts than spades: 50+5 = 55<br><BR>\n" );
document.write( " </SPAN>\n" );
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