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 #700867 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 10 characters, and 3 of them are S,<BR>\n" );
document.write( "so when picking your first character,<BR>\n" );
document.write( "the probability of picking an S would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F10 ALIGN=MIDDLE  ALT=\"3%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that, there would be 9 characters left, including two S characters.<BR>\n" );
document.write( "Then the probability id picking an S for last character,<BR>\n" );
document.write( "after having picked an S for fist character would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F9 ALIGN=MIDDLE  ALT=\"2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the probability that a rearrangements of the letters in STATISTICS<BR>\n" );
document.write( "would start and end with S is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F10%29%282%2F9%29=highlight%282%2F30%29 ALIGN=MIDDLE  ALT=\"%283%2F10%29%282%2F9%29=highlight%282%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "ANOTHER WAY:<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21=10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2 ALIGN=MIDDLE  ALT=\"10%21=10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible arrangements.<BR>\n" );
document.write( "If you labeled the letters so as to distinguish one S from another S, one T from another T, and one I from the other I, you would see that many different arrangements.<BR>\n" );
document.write( "If we are to make arrangements starting and ending with S,<BR>\n" );
document.write( "there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A2 ALIGN=MIDDLE  ALT=\"3%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to choose which S will be at either end,<BR>\n" );
document.write( "and there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%21=8%2A7%2A6%2A5%2A4%2A3%2A2 ALIGN=MIDDLE  ALT=\"8%21=8%2A7%2A6%2A5%2A4%2A3%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to arrange the 8 middle characters.<BR>\n" );
document.write( "That makes for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A8%21 ALIGN=MIDDLE  ALT=\"3%2A8%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > different arrangements starting and ending wit S,<BR>\n" );
document.write( "out of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21 ALIGN=MIDDLE  ALT=\"10%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible arrangements.<BR>\n" );
document.write( "That is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A2%2A8%21%2F10%21=%283%2A2%2A8%2A7%2A6%2A5%2A4%2A3%2A2%29%2F%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%29=3%2A2%2F%2810%2A9%29=2%2F30 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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