document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086637>Question 1086637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The letters of the word STATISTICS are arranged randomly.\r<BR>\n" );
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document.write( "What is the probability the arrangement will start and end with an S? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700865 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=700865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">There are 10 letters in the word STATISTICS.\r<BR>\n" );
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document.write( "So there are 10 slots needed to be filled. The first and last slot (slot1, slot10) are reserved for the letter S. There is only one way to do this. This is because the three S letters are not unique from one another.\r<BR>\n" );
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document.write( "The remaining middle 8 slots (slot2 through slot9) are open to be filled with 8 choices drawn from this list: {T,A,T,I,S,T,I,C}\r<BR>\n" );
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document.write( "There are 8! = 8*7*6*5*4*3*2*1 = 40,320 different ways to fill those 8 slots if we can tell the repeating letters apart.\r<BR>\n" );
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document.write( "Since we can't tell them apart, we have to divide by 3!*2! to deal with the fact that the letter \"T\" repeats three times and the letter \"I\" repeats twice.\r<BR>\n" );
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document.write( "We now have (40320)/(3!*2!)=(40320)/(6*2)=(40320)/(12)=3360\r<BR>\n" );
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document.write( "Meaning that there are 3,360 ways to arrange the letters so that the arrangement will start and end with an S\r<BR>\n" );
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document.write( "We will use the value 3360 later, so let's make A = 3360\r<BR>\n" );
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document.write( "If we ignore the restrictions, and simply count the number of arrangements, then we have (10!)/(3!*3!*2!) = 50400 different arrangements. \r<BR>\n" );
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document.write( "We'll call this value B = 50400\r<BR>\n" );
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document.write( "Divide the values of A and B to get A/B = 3360/50400 = 1/15\r<BR>\n" );
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document.write( "The answer as a fraction is <font color=red>1/15</font>\r<BR>\n" );
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document.write( "The answer in decimal form is approximately <font color=red>0.0667</font> (use a calculator to compute 1/15 = 0.0667)\r<BR>\n" );
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document.write( "The answer in percentage form is approximately <font color=red>6.67%</font> (move the decimal point over 2 spots to the right)\r<BR>\n" );
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document.write( "Edit: My initial answer was incorrect, but I have fixed it</font> </SPAN>\n" );
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