document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=666145>Question 666145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I pick 3 letters at a time from the word, MISSISSIPPI, how many combinations, I can get? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #414302 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=414302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a multinomial problem. You can think of this in two ways. There is the intuitive way, and then there is the general formula.\r<BR>\n" );
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document.write( "In either case, how many letters are in MISSISSIPPI? 11.\r<BR>\n" );
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document.write( "Now partition the word into its letters.\r<BR>\n" );
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document.write( "1 M<BR>\n" );
document.write( "4 Is<BR>\n" );
document.write( "4 Ss<BR>\n" );
document.write( "2 Ps<BR>\n" );
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document.write( "11 total letters\r<BR>\n" );
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document.write( "Since the order in which our letters are partitioned doesn't matter, we can start with any letter.\r<BR>\n" );
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document.write( "Let's start with M.\r<BR>\n" );
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document.write( "We want to choose 1 M out of 11 letters. There are (11 choose 1) ways to do this. Now we have 10 letters to choose from. Let's use I now.\r<BR>\n" );
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document.write( "(10 choose 4) ways to choose Is from the remaining letters.\r<BR>\n" );
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document.write( "Continuing in this fashion we get:\r<BR>\n" );
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document.write( "(11 choose 1)(10 choose 4)(6 choose 4)(2 choose 2)= 34650.\r<BR>\n" );
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document.write( "If you were to break this apart for the general case, you'd eventually get to this result:\r<BR>\n" );
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document.write( "Let N be the number of total things to choose from. Let n1,n2,n3,n4...nk be the separate k partitions.\r<BR>\n" );
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document.write( "Then we have that the total number of ways to choose n1,n2,n3,n4....nk things from N  is  N!/(n1! * n2! * n3! ... nk!).\r<BR>\n" );
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document.write( "Then we get 11!/(4!*4!*2!*1!) = 34650, as we would expect. </SPAN>\n" );
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