document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203031>Question 1203031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 3 books are picked from the shelf containing 5 novels 3 books of poems and a dictionary what is the prbability that the dictionary is selected.<BR>\n" );
document.write( "2) 2 novels and 1 book of poem are selected </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838267 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=838267\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "In addition to the solution to the first problem from the other tutor, using nCr numbers, here are two other more elementary ways to solve that one.<br><BR>\n" );
document.write( "These alternative methods only work for relatively simple problems like this one; however, they are useful methods for many similar problems.<br><BR>\n" );
document.write( "(1) Pick the books one at a time and find the probability that the dictionary is NOT selected; then the probability that it IS selected is 1 minus that probability.<br><BR>\n" );
document.write( "P(not selected first) = 8/9<BR>\n" );
document.write( "P(not selected first and not selected second) = (8/9)(7/8) = 7/9<BR>\n" );
document.write( "P(not selected first and not selected second and not selected third) = (8/9)(7/8)(6/7) = 6/9 = 2/3<br><BR>\n" );
document.write( "P(IS selected first or second or third) = 1 - 2/3 = 1/3<br><BR>\n" );
document.write( "(2) Pick the books one at a time and find the probability that the dictionary is selected either first or second or third.<br><BR>\n" );
document.write( "P(picked first) = 1/9<BR>\n" );
document.write( "P(not picked first; picked second) = (8/9)(1/8) = 1/9<BR>\n" );
document.write( "P(not picked first or second; picked third) = (8/9)(7/8)(1/7) = 1/9<br><BR>\n" );
document.write( "P(picked first or second or third) = 1/9 + 1/9 + 1/9 = 3/9 = 1/3<br><BR>\n" );
document.write( "Note solving your second problem by either of these methods would be very tedious because of the many different sequences in which the 2 novels and 1 book of poems could be selected.  The nCr method shown by the other tutor is far more efficient for this problem.<br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );