document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957472>Question 957472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> So, I forgot how to do permutations/combinations. I'm embarrassed, but whatever. 8 places, 30 objects, how many combinations? Can you show me how? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585084 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=585084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have 8 slots. Call them A through H\r<BR>\n" );
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document.write( "Slot A: 30 choices<BR>\n" );
document.write( "Slot B: 29 choices (once you pick something for slot A, you can't reuse it)<BR>\n" );
document.write( "Slot C: 28 choices<BR>\n" );
document.write( "Slot D: 27 choices<BR>\n" );
document.write( "Slot E: 26 choices<BR>\n" );
document.write( "Slot F: 25 choices<BR>\n" );
document.write( "Slot G: 24 choices<BR>\n" );
document.write( "Slot H: 23 choices\r<BR>\n" );
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document.write( "Multiply out all the numbers: 30*29*28*27*26*25*24*23 = 235,989,936,000\r<BR>\n" );
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document.write( "So if you wanted to find the permutation P(30,8), then the answer would be 235,989,936,000\r<BR>\n" );
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document.write( "However, you want the combination, so you use the formula\r<BR>\n" );
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document.write( "C(n,r) = [ P(n,r) ]/[ r! ]\r<BR>\n" );
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document.write( "So that means...\r<BR>\n" );
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document.write( "C(n,r) = [ P(n,r) ]/[ r! ]<BR>\n" );
document.write( "C(30,8) = [ P(30,8) ]/[ 8! ]<BR>\n" );
document.write( "C(30,8) = [ 235,989,936,000 ]/[ 8*7*6*5*4*3*2*1 ]<BR>\n" );
document.write( "C(30,8) = [ 235,989,936,000 ]/[ 40,320 ]<BR>\n" );
document.write( "C(30,8) = [ 235,989,936,000 ]/[ 40,320 ]<BR>\n" );
document.write( "C(30,8) = 5,852,925\r<BR>\n" );
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document.write( "So we got C(30,8) = 5,852,925\r<BR>\n" );
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document.write( "There are 5,852,925 different combinations (where order doesn't matter)\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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document.write( "------------------------------------------------------------------------------------------------------------------------ </SPAN>\n" );
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