document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174216>Question 1174216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a deck of 52 playing cards (jokers not allowed), how many five-card poker hands consisting of three of a kind and a pair (a full house) are possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799611 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=799611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here are a couple of different ways to calculate the number.  When working with probability, it is good to be able to see that two different paths lead to the same answer.<br><BR>\n" );
document.write( "First method....<br><BR>\n" );
document.write( "(1) choose 2 of the 13 ranks to be the ones in the hand;<BR>\n" );
document.write( "(2) choose 1 of those 2 to be the one of which there are 3;<BR>\n" );
document.write( "(3) choose 3 of the 4 of the first rank;<BR>\n" );
document.write( "(4) choose 2 of the 4 of the other rank<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2813%2C2%29%2AC%282%2C1%29%2AC%284%2C3%29%2AC%284%2C2%29+=+78%2A2%2A4%2A6+=+3744 ALIGN=MIDDLE  ALT=\"C%2813%2C2%29%2AC%282%2C1%29%2AC%284%2C3%29%2AC%284%2C2%29+=+78%2A2%2A4%2A6+=+3744\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Second method....<br><BR>\n" );
document.write( "(1) choose one of the 13 ranks to be the one with 3 cards of that rank;<BR>\n" );
document.write( "(2) choose 3 of the 4 cards of that rank;<BR>\n" );
document.write( "(3) choose one of the other 12 ranks to be the one with 2 cards;<BR>\n" );
document.write( "(4) choose 2 of the 4 cards of that rank<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2813%2C1%29%2AC%284%2C3%29%2AC%2812%2C1%29%2AC%284%2C2%29+=+13%2A4%2A12%2A6+=+3744 ALIGN=MIDDLE  ALT=\"C%2813%2C1%29%2AC%284%2C3%29%2AC%2812%2C1%29%2AC%284%2C2%29+=+13%2A4%2A12%2A6+=+3744\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );