document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=649593>Question 649593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Among the 2,598,960 possible five-card poker hands from a standard 52-card deck, how many contain AT LEAST ONE CLUB (complement of \"no clubs\")? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407019 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=407019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> N[at least one club]  = N[total ways] - N'[at least one club] = N[total ways] - N[no clubs]\r<BR>\n" );
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document.write( "There are 39 cards without a club. So there are 39 choose 5 = 575757 ways to not get a club.\r<BR>\n" );
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document.write( "There are 2598960 possible hands, leaving us with 2598960-575757 ways.\r<BR>\n" );
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document.write( "Which is 2023203 hands.\r<BR>\n" );
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