document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209380>Question 1209380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A combination lock has the integers 1 through 20 on its dial. Opening the lock requires a combination consisting of 3 of these integers, all different from one another and in a particular order. How many different combinations are possible for this lock?\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 #848719 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>6840</font>\r<BR>\n" );
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document.write( "20*19*18 = <font color=red>6840</font>\r<BR>\n" );
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document.write( "Explanation: <BR>\n" );
document.write( "Technically it should be called a permutation lock since order matters in a permutation. <BR>\n" );
document.write( "There are 20 choices for the first slot, 19 choices for the next, and 18 choices for the final slot. This countdown is happening since we cannot repeat values.<BR>\n" );
document.write( "Multiply those values to get the final answer.<BR>\n" );
document.write( "Another way to reach this answer is to use the nPr permutation formula with n = 20 and r = 3.<BR>\n" );
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