document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5927>Question 5927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I roll 5 regular dice out of a cup, what is<BR>\n" );
document.write( "1. The probability that I will get 5 of a kind.  I think the answer is 1 in 1296.\r<BR>\n" );
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document.write( "2. What is the probability that I will get two pair, i.e., 22335, 55422, even 33433 would count as two pair.  I come up with 1 in 34.56 rolls but I don't think this is correct.\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Bob Boose </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791223 by </B><A HREF=/tutors/aboutme.mpl?userid=pratapdas><B>pratapdas(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pratapdas><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=pratapdas><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. There are 6 possibilities to get 5 of a kind on 5 regular dices, i.e. all 1, all 2, all 3, all 4, all 5, and all 6. Each one has a probability of 1/6^5. Therefore, total prob. = 6/6^5 = 1/6^4 = 1/1296.\r<BR>\n" );
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document.write( "2. We choose 2 dices among 5 (5C2), 1 value among 6 to place on those 2 dices (6C1), then we choose 2 dices from the rest 3 (3C2), and again 1 value from rest 5 to place on those 2 dices (5C1), and lastly 1 value among rest 4 to put on the last dice (4C1)<BR>\n" );
document.write( "Total count = 5C2 * 6C1 *3C2 * 5C1 * 4C1 = 7200<BR>\n" );
document.write( "Prob = 7200/6^5 = 25/27 </SPAN>\n" );
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