document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118127>Question 118127</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201771314/algebrahomeworkh>Introductory Statistics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the following problem:<BR>\n" );
document.write( "A poker hand consistes of 5 cards dealt from an ordinary deck of 52 playing cards.<BR>\n" );
document.write( "a). How many poker hands are possible?<BR>\n" );
document.write( "b). How many different hands consisting of three kings and two queens are possible?<BR>\n" );
document.write( "c). The hand in part (b) is an example of a full house:  3 cards of one denomination and 2 of another.  How many different full houses are possible?<BR>\n" );
document.write( "d). Calculate the probability of being dealt a full house.<BR>\n" );
document.write( "This is dealing with the counting rules and using the combination rule and the permutations rule.<BR>\n" );
document.write( "Thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86235 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=86235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A poker hand consistes of 5 cards dealt from an ordinary deck of 52 playing cards.<BR>\n" );
document.write( "a). How many poker hands are possible?<BR>\n" );
document.write( "52C5 = 2,598,960<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "b). How many different hands consisting of three kings and two queens are possible?<BR>\n" );
document.write( "[4C3*4C2] = 4*6 = 24<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "c). The hand in part (b) is an example of a full house: 3 cards of one denomination and 2 of another. How many different full houses are possible?<BR>\n" );
document.write( "Pick a card type: 13 ways<BR>\n" );
document.write( "Pick 3 of the 4 cards: 4C3=4<BR>\n" );
document.write( "Pick a 2nd card type: 12 ways<BR>\n" );
document.write( "Pick 2 of the 4 cards: 4C2= 6<BR>\n" );
document.write( "Total = 13*12*4*6 = 3744 full houses possible.<BR>\n" );
document.write( "----------------\r<BR>\n" );
document.write( "\n" );
document.write( "d). Calculate the probability of being dealt a full house.<BR>\n" );
document.write( "3744/2,598,960<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" );