document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=499008>Question 499008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boy found a bicycle lock for which the combination was unknown.  The correct combination is a four-digit number.  The digits are selected from 1, 2, 3, 5, 6, and 7.<BR>\n" );
document.write( "a.What is the probability that he can open the lock by putting four random numbers in for the combination?<BR>\n" );
document.write( "b.What is the probability that he can open the lock at random if he knows that the combination is an odd number?<BR>\n" );
document.write( "c.What is the probability that he can open the lock at random if he knows that the numbers in the combination cannot be repeated? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #337324 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=337324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "There are 6 choices for each digit<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A6%2A6%2A6+=+1296+ ALIGN=MIDDLE  ALT=\"+6%2A6%2A6%2A6+=+1296+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The boy has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F1296+ ALIGN=MIDDLE  ALT=\"+1%2F1296+\"   DISABLED_style= \"max-width:90%; height:auto;\" > probability of getting<BR>\n" );
document.write( "the right combination<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "If he knows the number is odd, then the last digit <BR>\n" );
document.write( "cannot be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "choices for the last digit<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A6%2A6%2A4+=+864+ ALIGN=MIDDLE  ALT=\"+6%2A6%2A6%2A4+=+864+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F864+ ALIGN=MIDDLE  ALT=\"+1%2F864+\"   DISABLED_style= \"max-width:90%; height:auto;\" > probability of randomly <BR>\n" );
document.write( "getting the right odd combination if he knows<BR>\n" );
document.write( "the combination is odd<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "If numbers can't be repeated<BR>\n" );
document.write( "The number of choices are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A5%2A4%2A3+=+360+ ALIGN=MIDDLE  ALT=\"+6%2A5%2A4%2A3+=+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F360+ ALIGN=MIDDLE  ALT=\"+1%2F360+\"   DISABLED_style= \"max-width:90%; height:auto;\" > probability of getting the<BR>\n" );
document.write( "right combination if he knows digits can't be <BR>\n" );
document.write( "repeated </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );