document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139895>Question 1139895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi can someone help me solve this please? I got the first answer right on figuring out how many possible combinations of numbers there were on the lock but I am struggling with figuring out the answers to b and c. Thanks. \r<BR>\n" );
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document.write( "My combination bicycle lock has four wheels, each of which has the numbers 0 through 13. Exactly one combination of numbers (in order) on the wheels (7-2-10-6, e.g.) will open the lock.<BR>\n" );
document.write( "How many possible combinations of numbers are there on my bicycle lock?\r<BR>\n" );
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document.write( "(b) Suppose that I have forgotten my combination. At random I try 1-2-3-4. What is the probability that the lock will open with this combination? (Enter your probability as a fraction.)\r<BR>\n" );
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document.write( "(c) Out of frustration I try at random 25 different combinations. What is the probability that 1 of these 25 efforts will open the lock? (Enter your probability as a fraction.)<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 #760389 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52776)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "(a)  The total number of all possible combinations of numbers in this case is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%5E4 ALIGN=MIDDLE  ALT=\"14%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 38416.\r\n" );
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document.write( "     It is because there are 14 possible independent opportunities in each of 4 positions.\r\n" );
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document.write( "(b)  The probability that every (any) fixed concrete combination will open the lock is therefore  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F14%5E4 ALIGN=MIDDLE  ALT=\"1%2F14%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F38416 ALIGN=MIDDLE  ALT=\"1%2F38416\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "     The probability that the combination {1-2-3-4} is the happy key is therefore also  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F14%5E4 ALIGN=MIDDLE  ALT=\"1%2F14%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F38416 ALIGN=MIDDLE  ALT=\"1%2F38416\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "(c)  If you try 25 different combinations of 4 numbers, the probability to open the lock is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F14%5E4 ALIGN=MIDDLE  ALT=\"25%2F14%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F38416 ALIGN=MIDDLE  ALT=\"25%2F38416\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "I answered ALL YOUR QUESTIONS.\r<BR>\n" );
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document.write( "Do not forget to post your \"THANKS\" to me immediately after reading my post.\r<BR>\n" );
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document.write( "By the way, this problem came to the forum some days ago, and I answered and solved it under this link\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1139207.html\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;What is or what was the need to post it again ?\r<BR>\n" );
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