document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169916>Question 1169916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can the 3-Senator committee be formed such that no two Senators are from the same state? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794763 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=794763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are three slots or seats to fill on this committee.\r<BR>\n" );
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document.write( "For the first slot, we have 100 choices since we have 2*50 = 100 senators.<BR>\n" );
document.write( "After that person is picked, there are 98 choices left. Why 98 and not 99? Because we cannot pick a senator from the same state as the first person selected.\r<BR>\n" );
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document.write( "For example, let's say we pick a senator from Michigan to fill the first seat. The other senator from Michigan cannot be selected if we want this three-person committee to not have two members from the same state.\r<BR>\n" );
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document.write( "So again we have 98 choices for the second slot.\r<BR>\n" );
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document.write( "Then whoever goes in the second slot will lower the amount of choices down to 96 for similar reasoning as before.\r<BR>\n" );
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document.write( "Overall we have 100*98*96 = 940,800 permutations possible \r<BR>\n" );
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document.write( "Since order doesn't matter, we divide by 3! = 3*2*1 = 6 to get (940,800)/6 = 156,800\r<BR>\n" );
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document.write( "Note how there are 6 ways to arrange a group of three items<BR>\n" );
document.write( "{A,B,C}<BR>\n" );
document.write( "{A,C,B}<BR>\n" );
document.write( "{B,A,C}<BR>\n" );
document.write( "{B,C,A}<BR>\n" );
document.write( "{C,A,B}<BR>\n" );
document.write( "{C,B,A}<BR>\n" );
document.write( "All six sets listed above are the same set since all have A,B,C in some order. The order doesn't matter on a committee. No member outranks another. All that matters is the group overall.\r<BR>\n" );
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document.write( "Answer: 156,800<BR>\n" );
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document.write( " </SPAN>\n" );
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