document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231490>Question 231490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different 5-card poker hands would contain only cards of a single suit?\r<BR>\n" );
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document.write( "I know there are 52 cards in a deck and there are 4 different suits with 13 cards in each suit. From here, I am lost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171309 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How many different 5-card poker hands would contain only cards of a single suit? <BR>\n" );
document.write( "I know there are 52 cards in a deck and there are 4 different suits with 13 cards in each suit. From here, I am lost.<BR>\n" );
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document.write( "It's 5 cards out of 13.<BR>\n" );
document.write( "The 1st is 1 of 13, then 1 of 12, etc = 13*12*11*10*9<BR>\n" );
document.write( "= 154,440<BR>\n" );
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document.write( "But, since 2, 3, 4, 5, 6 is the same as 6,5,4,3,2 it's necessary to divide by 5*4*3*2*1 = 120<BR>\n" );
document.write( "--> 154440/120 = 1287 possibilities.<BR>\n" );
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document.write( "To be more formal, it's <BR>\n" );
document.write( "13!/(5!*(13-5)!)<BR>\n" );
document.write( "! is factorial.  5! = 5*4*3*2*1, etc.<BR>\n" );
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