document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725503>Question 725503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the probability that a poker hand (5 card draw) contains nothing but aces and eights?\r<BR>\n" );
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document.write( "-I've went to my instructor for help and he told me that it would be a combination problem.\r<BR>\n" );
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document.write( "-The way I was doing it was that I wrote out the elements:<BR>\n" );
document.write( "{1(A),4(8)},{2(A),3(8)},{3(A),2(8)},{4(A),1(8)}\r<BR>\n" );
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document.write( "Then I wrote my answer as (1/52)*(1/51)*(1/50)*(1/49)*(1/48) because a poker hand is without replacement (showing that I am not returning an ace or eight back to the deck).\r<BR>\n" );
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document.write( "-I've tried both combination formulas that I have and it is not giving me an answer less than or equal to 1 (since it is a probability problem).  \r<BR>\n" );
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document.write( "the two combination formulas I have are: \r<BR>\n" );
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document.write( "n!/[r!(n-r)!] (without replacement)\r<BR>\n" );
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document.write( "(r+(n-1))  <BR>\n" );
document.write( "(  r    )    (with replacement) *(trying to show a combination \"()\" instead of a fraction or two separate \"()\")*\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444174 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=444174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the probability that a poker hand (5 card draw) contains nothing but aces and eights? <BR>\n" );
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document.write( "I'm assuming there are at least one ace and 1 eight in each hand.<BR>\n" );
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document.write( "Successful combinations in ace/8's order:<BR>\n" );
document.write( "1/4 ; 2/3 ; 3/2 ; 4/1<BR>\n" );
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document.write( "# of ways to get each combination:<BR>\n" );
document.write( "1/4::: 4C1*4C4 = 4*1 = 4<BR>\n" );
document.write( "2/3::: 4C2*4C3 = 7*4 = 28<BR>\n" );
document.write( "3/2::: 4C3*4C2 = 4*7 = 28<BR>\n" );
document.write( "4/1::: 4C4*4C1 = 1*4 = 4<BR>\n" );
document.write( "Total number of 5 card hands with at least one ace and one eight: 64<BR>\n" );
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document.write( "Total number of 5 card hands: 52C5 = 2598960<BR>\n" );
document.write( "Probability = 66/2598960 = 0.00002539<BR>\n" );
document.write( "==========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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