document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168922>Question 168922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How may FIVE card poker hands are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124567 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=124567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How may FIVE card poker hands are there?<BR>\n" );
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document.write( "The 1st card can be one of 52, the 2nd will be 1 out of 51, etc, so we get 52*51*50*49*48 = 311,875,200.<BR>\n" );
document.write( "But, drawing 3 4 5 6 7 is the same hand as drawing 3 7 5 6 4 (the same 5 cards drawn in a different order), so we have to divide by 5*4*3*2*1 = 5! = 120.<BR>\n" );
document.write( "That gives the number of different hands = 2,598,960.<BR>\n" );
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document.write( "This is based on the assumption that the same card in a different suit makes a different hand.  For example, a full house with 3 Kings, the 10 of Hearts and the 10 of Spades, is viewed as different from a hand with any of the 5 cards exchanged for the same card of a different suit.  It has no effect on where it's a winning or losing hand in poker.<BR>\n" );
document.write( "Whether this assumption is valid is not specified.<BR>\n" );
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