document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89947>Question 89947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many five-poker hands consisting of the following distribution are there?<BR>\n" );
document.write( "a- aflush ( all five cards of a signle suit)<BR>\n" );
document.write( "b- theree of kind (three aces and two other cards)<BR>\n" );
document.write( "c- two pairs ( two aces, two kings and one other card)<BR>\n" );
document.write( "d- A straight ( all five cards in a sequence) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65307 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=65307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how many five-poker hands consisting of the following distribution are there?<BR>\n" );
document.write( "a- aflush ( all five cards of a signle suit)<BR>\n" );
document.write( "# of ways to pick a suit = 4<BR>\n" );
document.write( "# of ways to get 5 of the 13 cards 13C5<BR>\n" );
document.write( "Total # of flush hands = 4*13C5<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "b- three of kind (three aces and two other cards)<BR>\n" );
document.write( "# of ways to pick three aces = 4C3 = 4<BR>\n" );
document.write( "# of ways to pick two other cards = 48C2<BR>\n" );
document.write( "# of ways full house hands = 4*48C2<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "c- two pairs ( two aces, two kings and one other card)<BR>\n" );
document.write( "# of ways to pick two aces = 4C2 = 6<BR>\n" );
document.write( "# of ways to pick two kings = 4C2 = 6<BR>\n" );
document.write( "# of ways to pick one other card = 44C1 = 44<BR>\n" );
document.write( "Total # of ways to get 2 aces, 2 kings, one other = 6^2*44<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "d- A straight ( all five cards in a sequence)<BR>\n" );
document.write( "# of ways to get a straight pattern of 5 cards = 9<BR>\n" );
document.write( "# of ways to pick the 5 cards 4^5<BR>\n" );
document.write( "# of straight hands = 9*4^5<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );