document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205238>Question 1205238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different arrangements can be formed by taking 4 letters from the word<BR>\n" );
document.write( "STATISTICS? Assume that the letters are taken without replacement. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841909 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are 5 different letters: 3 each of S and T, 2 of I, and 1 each of A and C.<br><BR>\n" );
document.write( "To choose 4 letters, we have the following different cases to consider:<BR>\n" );
document.write( "(1) 3 of one letter and 1 of a different letter<BR>\n" );
document.write( "(2) 2 each of two different letters<BR>\n" );
document.write( "(3) 2 of one letter and 1 each of two other letters<BR>\n" );
document.write( "(4) 4 different letters<br><BR>\n" );
document.write( "(1) 3 and 1.  We need to...<BR>\n" );
document.write( "choose one of the two letters that occurs 3 times: C(2,1)=2<BR>\n" );
document.write( "choose one of the other 4 letters: C(4,1)=4<BR>\n" );
document.write( "arrange the 4 letters in any of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%21%2F%28%283%21%29%281%21%29%29=4 ALIGN=MIDDLE  ALT=\"4%21%2F%28%283%21%29%281%21%29%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways<br><BR>\n" );
document.write( "Number of arrangements: (2)(4)(4) = 32<br><BR>\n" );
document.write( "(2) 2 and 2.  We need to...<BR>\n" );
document.write( "choose two of the three letters that occurs 2 or more times: C(3,2)=3<BR>\n" );
document.write( "arrange the 4 letters in any of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%21%2F%28%282%21%29%282%21%29%29=6 ALIGN=MIDDLE  ALT=\"4%21%2F%28%282%21%29%282%21%29%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways<br><BR>\n" );
document.write( "Number of arrangements: (3)(6) = 18<br><BR>\n" );
document.write( "(3) 2, 1, and 1.  We need to...<BR>\n" );
document.write( "choose one of the three letters that occurs 2 or more times: C(3,1)=3<BR>\n" );
document.write( "choose two of the other 4 letters: C(4,2)=6<BR>\n" );
document.write( "arrange the 4 letters in any of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%21%2F%28%282%21%29%281%21%29%281%21%29%29=12 ALIGN=MIDDLE  ALT=\"4%21%2F%28%282%21%29%281%21%29%281%21%29%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways<br><BR>\n" );
document.write( "Number of arrangements: (3)(6)(12) = 216<br><BR>\n" );
document.write( "(4) 1, 1, 1, and 1.  We need to...<BR>\n" );
document.write( "choose any 4 of the 5 letters: C(5,4)=1<BR>\n" );
document.write( "arrange the 4 letters in any of 4! = 24 ways<br><BR>\n" );
document.write( "Number of arrangements: (5)(24) = 120<br><BR>\n" );
document.write( "Total number of arrangements: 32+18+216+120 = 386<br><BR>\n" );
document.write( "ANSWER: 386<br><BR>\n" );
document.write( " </SPAN>\n" );
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