document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48481>Question 48481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A firm has an opening for 3 computer programmers and there are 20 applicants.  In how many different ways can the job be filled? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #32072 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=32072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is slightly more tricky.\r<BR>\n" );
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document.write( "Lets assume this is just like the other questions you asked. I shall answer it that way and then explain the problem and then correct my answer.\r<BR>\n" );
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document.write( "So... 20 people apply for a job. How many could get the first place? Answer is any of the 20.<BR>\n" );
document.write( "And the second place? Answer is 19<BR>\n" );
document.write( "And the third place? Answer is 18\r<BR>\n" );
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document.write( "So we have 20*19*18.\r<BR>\n" );
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document.write( "However, this is way too large because of the nature of what is being asked. Lets assume that applicants A, B and C are the ones who actually get the 3 jobs.\r<BR>\n" );
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document.write( "From the 20*19*18 answer - this includes the permutations ABC, ACB, BAC, BCA, CAB, CBA.\r<BR>\n" );
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document.write( "However all these 6 variations are the same: A,B and C got the job in all 6 cases. So our 20*19*18 answer is too big by 6 times, since the combination ABC is an answer just once. In other words, the order does not matter here.\r<BR>\n" );
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document.write( "So, correctly we have (20*19*18)/3! where the 3! gives us 6 and the 3 comes from the fact that we have 3 \"jobs\" to allocate.\r<BR>\n" );
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document.write( "This is where Permutations and Combinations are difficult... spotting the difference and for me it is tricky too, but i have had 20 years practice. Best way is to take it slowly and think about the physical nature of what is being asked, like i have written here.\r<BR>\n" );
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document.write( "jon<BR>\n" );
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