document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098384>Question 1098384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A shipment of 22 fuses contains 3 defective fuses. A quality control specialist chooses a sample of 7 fuses from the shipment.\r<BR>\n" );
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document.write( "a. How many possible choices of 7 fuses can be made?<BR>\n" );
document.write( "b. How many of these possible selections will not contain any defective fuses?<BR>\n" );
document.write( "c. How many of the possible selections will contain at least one defective fuse?<BR>\n" );
document.write( "d. How many of the possible selections will contain exactly one defective fuse?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713203 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A shipment of 22 fuses contains 3 defective fuses. A quality control specialist chooses a sample of 7 fuses from the shipment.<BR>\n" );
document.write( "a. How many possible choices of 7 fuses can be made?<BR>\n" );
document.write( " Combinations of 22, taking 7 at a time = 22x21x20x19x18x17x16 / (7x6x5x4x3x2) = 170544.<BR>\n" );
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document.write( "b. How many of these possible selections will not contain any defective fuses?<BR>\n" );
document.write( "As there are 22 - 3 =18 fuses that are not defective, with those 18 you can make<BR>\n" );
document.write( "18x17x16x15x14x13x12 / (7x6x5x4x3x2) = 50388<BR>\n" );
document.write( "(combinations of 18, taking 7 at a time) sets of 7 fuses not containing any defective fuse.<BR>\n" );
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document.write( "c. How many of the possible selections will contain at least one defective fuse?<BR>\n" );
document.write( "There are 170544 - 50388 = 120156<BR>\n" );
document.write( "possible selections of 7 fuses (those not counted in part b above) that contain one or more defective fuses.<BR>\n" );
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document.write( "d. How many of the possible selections will contain exactly one defective fuse?<BR>\n" );
document.write( "3 x 18x17x16x15x14x13x12 / (6x5x4x3x2) = 3 x 27132 = 81396 .<BR>\n" );
document.write( "The number of possible sets of 6 not-defective fuses is<BR>\n" );
document.write( "combinations of 18, taking 6 at a time = 18x17x16x15x14x13x12 / (6x5x4x3x2) = 27132.<BR>\n" );
document.write( "To each of those you couls add one of the 3 defective fuses to make all possible selections containing exactly one defective fuse. </SPAN>\n" );
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