document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=918991>Question 918991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Having a lot of trouble with understanding Probabilities, Combinations, and Permutations. Please help.  When I looked up a problem similar to this one I saw something like ! by the numbers (5! + 4! = 126) which was pretty confusing.\r<BR>\n" );
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document.write( "Exact Question: How many different 5-person basketball teams can a coach choose from among 7 players?\r<BR>\n" );
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document.write( "I thought all you had to do was multiply 5 x 7 which gives you 35, but I'm doubting the answer.\r<BR>\n" );
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document.write( "Thank you so so very much for reading this question and if you do proceed to answer please answer which ALOT detail. Sorry if I sound demanding, I can't stress how much probability, combination, and premutation confuses me. >.< </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557373 by </B><A HREF=/tutors/aboutme.mpl?userid=Hawksfan><B>Hawksfan(61)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Hawksfan><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=Hawksfan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=557373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In this problem you will either have a permutation or a combination.  But how do you tell?   \r<BR>\n" );
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document.write( "With a permutation, the order or how the items are arranged matters greatly.<BR>\n" );
document.write( "With a combination, the order doesn't matter at all.  \r<BR>\n" );
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document.write( "The example above talks about a problem where it doesn't matter what<BR>\n" );
document.write( "order the players are in.  We can have the 5 player teams in any order. <BR>\n" );
document.write( "Therefore its a combination.  \r<BR>\n" );
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document.write( "The formula for a combination is  nCr = n!/(n-r)!  \r<BR>\n" );
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document.write( "where n =  total number of items<BR>\n" );
document.write( "r =  number of items of subgroup \r<BR>\n" );
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document.write( "examples of n! (separate from the problem) <BR>\n" );
document.write( "4! = 4*3*2*1<BR>\n" );
document.write( "9! = 9*8*7*6*5*4*3*2*1<BR>\n" );
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document.write( " nCr = n!/r!(n-r)!\r<BR>\n" );
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document.write( "n = 7,  r =5  \r<BR>\n" );
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document.write( "7C5 = 7!/5!(7-5)!  = 7*6*5*4*3*2*1/[(5*4*3*2*1)(2*1)]<BR>\n" );
document.write( "7C5 =  7*6/2<BR>\n" );
document.write( "    = 21 </SPAN>\n" );
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