document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145215>Question 145215</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321206002/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Help! Please-Thanks\r<BR>\n" );
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document.write( "13. (4 pts) At an annual flower show, 6 different entries are to be arranged in a row. <BR>\n" );
document.write( "a) How many different arrangements of the entries are possible? 6!<BR>\n" );
document.write( "b) If the owners of the 1st, 2nd, and 3rd place entries will be awarded prizes of $100, $50, and $25 respectively, how many ways can the prizes be awarded?  6 items taken 3 at a time 6*5*4 = 120 ??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105890 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=105890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A5%2A4%2A3%2A2%2A1+=+720 ALIGN=MIDDLE  ALT=\"6%2A5%2A4%2A3%2A2%2A1+=+720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) You're looking for combinations here, not arrangements, because<BR>\n" );
document.write( "you don't care how the prize winners are arranged, once they have<BR>\n" );
document.write( "their prizes. You need the formula for combinations of 3 things<BR>\n" );
document.write( "chosen from 6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%21+%2F+%283%21+%2A%286-3%29%21%29+=+20 ALIGN=MIDDLE  ALT=\"6%21+%2F+%283%21+%2A%286-3%29%21%29+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It's easy to check:<BR>\n" );
document.write( "Call the entries ABCDEF<BR>\n" );
document.write( "The possible combinations:<BR>\n" );
document.write( "Including A<BR>\n" );
document.write( "ABC ACD ADE AEF<BR>\n" );
document.write( "ABD ACE ADF<BR>\n" );
document.write( "ABE ACF<BR>\n" );
document.write( "ABF<BR>\n" );
document.write( "Including B (without repeats)<BR>\n" );
document.write( "BCD BDE BEF<BR>\n" );
document.write( "BCE BDF<BR>\n" );
document.write( "BCF<BR>\n" );
document.write( "Including C (without repeats)<BR>\n" );
document.write( "CDE CEF<BR>\n" );
document.write( "CDF<BR>\n" );
document.write( "Including D (without repeats)<BR>\n" );
document.write( "DEF<BR>\n" );
document.write( "(Note that E and F are already combined with A,B,C,and D) <BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "These add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > combinations </SPAN>\n" );
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