document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256421>Question 256421</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188529 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected?<BR>\n" );
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document.write( "The 1st selection is 1 of 7, then 1 of 6, then 1 of 5, etc<BR>\n" );
document.write( "7*6*5*4*3 = 2520<BR>\n" );
document.write( "But selecting A, B, C, D and E is the same as B, C, E, D and A.  Person A has 5 chances to be selected.  The 2nd has 4 chances to be selected, etc.  5*4*3*2*1 = 120.<BR>\n" );
document.write( "The number of possible combinations is 2520/120 = 21<BR>\n" );
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document.write( "To make it simpler, find the number of different ways 2 people are not selected:<BR>\n" );
document.write( "The 1st is one of 7, the 2nd is one of 6 --> 7*6 = 42.<BR>\n" );
document.write( "A and B is the same as B and A, so divide by 2<BR>\n" );
document.write( "42/2 = 21.\r<BR>\n" );
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