document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175393>Question 175393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different permutations can you make with the letters in the word seventeen? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130530 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=130530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula for a permutation of a set of x units out of a possible set of n units is given by the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-x%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-x%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you have 9 possible letters, so n would = 9 in this case.<BR>\n" );
document.write( "you will be extracting a set of 9 letters from this, so x would also be 9 in this case.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the number of possible ways this set of 9 letters can be arranged if order is important (permutation is an ordered set) are then given by the equation:<BR>\n" );
document.write( "9! / (9-9)!<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "9! / 0!<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "9!<BR>\n" );
document.write( "because 0! = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the resultant answer would be 362880<BR>\n" );
document.write( "---<BR>\n" );
document.write( "this answer assumes that the same letter can be used more than once.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the word seventeen has 4 e's and 2 n's<BR>\n" );
document.write( "to distinguish between them you would have to label them differently.<BR>\n" );
document.write( "something like:<BR>\n" );
document.write( "e1, e2, e3, e4, e5<BR>\n" );
document.write( "n1, n2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "you can also assign numbers to each letter so that they show up as unique.<BR>\n" );
document.write( "something like:<BR>\n" );
document.write( "s = 1, first e = 2, v = 3, second e = 4, etc.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "if multiple occurrences of the same letter are not allowed, then the problem becomes different.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the assumption here would be that multiple occurrences of the same letter count as one occurrence.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "in that case, you have 5 unique letters to choose from.<BR>\n" );
document.write( "those are:<BR>\n" );
document.write( "s, e, v, n, t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the number of permutations you could make with these letters would be 5! which equals 120<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to help you see this, take a word with smaller number of letters in it.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "let the word \"see\" be the problem.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "assuming the ssme letter can be used more than once, the number of permutations would be 3! = 6<BR>\n" );
document.write( "let s = 1, first e = 2, second e = 3<BR>\n" );
document.write( "this will make it easier to show:<BR>\n" );
document.write( "the individual permutations are:<BR>\n" );
document.write( "123<BR>\n" );
document.write( "132<BR>\n" );
document.write( "213<BR>\n" );
document.write( "231<BR>\n" );
document.write( "312<BR>\n" );
document.write( "321<BR>\n" );
document.write( "---<BR>\n" );
document.write( "assume that multiple occurrences of the same letter count as one occurrence of that letter.<BR>\n" );
document.write( "then the possible letters that can be used are s and e only.<BR>\n" );
document.write( "this would be 2!<BR>\n" );
document.write( "let s = 1, e = 2<BR>\n" );
document.write( "permutations are:<BR>\n" );
document.write( "12<BR>\n" );
document.write( "21<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the answer to your question is therefore:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "if multiple occurrences of the same letter count as a separate occurrence of tht letter, then the number of permutations is 9! = 362880<BR>\n" );
document.write( "---<BR>\n" );
document.write( "if multiple occurrences of the same letter count as 1 occurrence of that letter, then the number of permutations is 5! = 120<BR>\n" );
document.write( "---<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );