document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199915>Question 1199915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that the student has a cup with 10 writing implements: 5 pencils, 3 ball point pens, and 2 felt-tip pens.\r<BR>\n" );
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document.write( "(1) In how many ways can the student select 4 writing implements? \r<BR>\n" );
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document.write( "(2) In how many ways can the selection be made if no more than one ball point pen is selected? \r<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 #833903 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) choose 4 implements out of 10 total: C(10,4) = 210<br><BR>\n" );
document.write( "(2) choose 1 ball point pen and 3 of the other 7 implements, or 0 ball point pens and 4 of the other 7: C(3,1)*C(7,3) + C(3,0)*C(7,4) = 3*35 + 1*35 = 140<br><BR>\n" );
document.write( "You can get good practice performing this kind of calculations by finding the number of ways of getting 2 or 3 ball point pens and verifying that the total number of ways of choosing 4 of the implements, using any number of ball point pens, is equal to the total number of ways, 210:<br><BR>\n" );
document.write( "2 ball point pens and 2 of the other 7: C(3,2)*C(7,2) = 3*21 = 63<BR>\n" );
document.write( "3 ball point pens and 1 of the other 7: C(3,3)*C(7,1) = 1*7 = 7<br><BR>\n" );
document.write( "140+63+7 = 210<br><BR>\n" );
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