document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098383>Question 1098383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After being put into service, some buses manufactured by a XYZ Company have developed cracks on the underside of the main frame. Suppose a particular province has 23 of these buses, and cracks have actually appeared in 12 of them.\r<BR>\n" );
document.write( "\n" );
document.write( "a. How many ways are there to select a sample of 10 buses from the 23 for a thorough inspection?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b. In how many ways can a sample of 7 buses contain exactly 3 with visible cracks?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713204 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=713204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> After being put into service, some buses manufactured by a XYZ Company have developed cracks on the underside of the main frame. Suppose a particular province has 23 of these buses, and cracks have actually appeared in 12 of them.<BR>\n" );
document.write( "a. How many ways are there to select a sample of 10 buses from the 23 for a thorough inspection?<BR>\n" );
document.write( " Combinations of 23, taking 10 at a time = 23x22x21x20x19x18x17x16x15x14 / (10x9x8x7x6x5x4x3x2) = 1144066.<BR>\n" );
document.write( " <BR>\n" );
document.write( "b. In how many ways can a sample of 7 buses contain exactly 3 with visible cracks?<BR>\n" );
document.write( " The number of possible samples of 7 buses containing exactly 3 buses with visible cracks is<BR>\n" );
document.write( "220 x 330 =7260.<BR>\n" );
document.write( "because there are 12 buses with visible cracks,<BR>\n" );
document.write( "from which you can make 12x11x10 / (3x2) = 220 different sets,<BR>\n" );
document.write( "and there are 23 - 12 = 11 buses without visible cracks,<BR>\n" );
document.write( "from which you can make 11X10x9x8 / (4x3x2) = 330 different sets,<BR>\n" );
document.write( "so there are 22 x 330 = 7260 ways you can pair  one set of each kind to make<BR>\n" );
document.write( "a sample of 7 buses containing exactly 3 buses with visible cracks. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );