document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144493>Question 144493</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078659809/algebrahomeworkh>Algebra 2 (California Edition)</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A shipment of ten television sets contains 3 defective sets. How many ways can a hospital purchase 4 of these sets and recieves at least 2 of the defective sets? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105273 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=105273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem might be easier to approach if you<BR>\n" );
document.write( "ask the opposite question:<BR>\n" );
document.write( "\"How many ways can the hospital purchase 4 of the 10<BR>\n" );
document.write( "sets and only get 1 of the defective sets or none of<BR>\n" );
document.write( "the defective sets?\"<BR>\n" );
document.write( "If I don't get any defective sets, then there are<BR>\n" );
document.write( "7 possible sets for the 1st one, 6 possible sets for<BR>\n" );
document.write( "the 2nd one, 5 for the 3rd, and 4 for the 4th<BR>\n" );
document.write( "The number of different combinations is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+7%2A6%2A5%2A4 ALIGN=MIDDLE  ALT=\"a+=+7%2A6%2A5%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "If I know I'm going to have 1 defective set, that means<BR>\n" );
document.write( "I don't have 4 to choose from for the last set, I only<BR>\n" );
document.write( "have the 3 defective ones, so the number of combinations<BR>\n" );
document.write( "with 1 defective set is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+7%2A6%2A5%2A3 ALIGN=MIDDLE  ALT=\"b+=+7%2A6%2A5%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "Then I have to ask, \"If I include ALL the possible combinations<BR>\n" );
document.write( "whether a set is defective or not, how many combinations<BR>\n" );
document.write( "are there? That answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+10%2A9%2A8%2A7 ALIGN=MIDDLE  ALT=\"c+=+10%2A9%2A8%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "Now if I add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, I get the number of combinations<BR>\n" );
document.write( "that I DON'T want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+=+7%2A6%2A5%2A4+%2B+7%2A6%2A5%2A3 ALIGN=MIDDLE  ALT=\"a+%2B+b+=+7%2A6%2A5%2A4+%2B+7%2A6%2A5%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+=+840+%2B+630 ALIGN=MIDDLE  ALT=\"a+%2B+b+=+840+%2B+630\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+=+1470 ALIGN=MIDDLE  ALT=\"a+%2B+b+=+1470\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "My answer should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+-+%28a+%2B+b%29 ALIGN=MIDDLE  ALT=\"c+-+%28a+%2B+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+10%2A9%2A8%2A7 ALIGN=MIDDLE  ALT=\"c+=+10%2A9%2A8%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+5040 ALIGN=MIDDLE  ALT=\"c+=+5040\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5040+-+1470+=+3570 ALIGN=MIDDLE  ALT=\"5040+-+1470+=+3570\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If I'm right, there are 3570 different combinations of 4 sets that<BR>\n" );
document.write( "include at least 2 defective ones. As with any problem like this,<BR>\n" );
document.write( "reasoning can off, so see if you agree. <BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "I thought this one over, and decided that I solved<BR>\n" );
document.write( "for all possible ARRANGEMENTS of the TVs in question, as if it<BR>\n" );
document.write( "made a difference which came 1st, 2nd, etc, which it doesn't<BR>\n" );
document.write( "So change <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2A6%2A5%2A4%29%2F%284%2A3%2A2%2A1%29+=+35 ALIGN=MIDDLE  ALT=\"%287%2A6%2A5%2A4%29%2F%284%2A3%2A2%2A1%29+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Change <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%287%2A6%2A5%29%2F%283%2A2%2A1%29%29%2A3+=+105 ALIGN=MIDDLE  ALT=\"%28%287%2A6%2A5%29%2F%283%2A2%2A1%29%29%2A3+=+105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Change <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%29%2F%284%2A3%2A2%2A1%29+=+210 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%29%2F%284%2A3%2A2%2A1%29+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+-+%28105+%2B+35%29+=+70 ALIGN=MIDDLE  ALT=\"210+-+%28105+%2B+35%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 70 different combinations of 4 sets that<BR>\n" );
document.write( "include at least 2 defective ones.<BR>\n" );
document.write( "Of course, unless I'm wrong again. Check the answer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );