document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995031>Question 995031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "Let's say I have three letters; A, B and C. I need to know the formula how to count the number of all possible combinations using A, B and C, the letters can be repeated and the order of the letters is important (e.g. ABC and BCA are not the same).\r<BR>\n" );
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document.write( "All the way here I'm pretty confident I can solve this alone. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3 ALIGN=MIDDLE  ALT=\"3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > right?\r<BR>\n" );
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document.write( "Moving on, what if the number of digits can be 1, 2 or 3? (e.g. A, B, C, AA, AB, ..., AAA, AAB, ABC, ... )<BR>\n" );
document.write( "Is there a way to count that any faster way than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3+%2B+3%5E2+%2B+3%5E1 ALIGN=MIDDLE  ALT=\"3%5E3+%2B+3%5E2+%2B+3%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "It is very time consuming if there can be any more than three digits in the answer and I have to manually solve it as shown above.\r<BR>\n" );
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document.write( "Thank you for your time! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613917 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For A, B, C, the maximum number of combinations is<BR>\n" );
document.write( "2*3^0 + 2*3^1 + 2*3^2 + 1 or<BR>\n" );
document.write( "2[(3^0)+(3^1)+(3^2)]+1 =<BR>\n" );
document.write( "2[1+3+9]+1 = 27\r<BR>\n" );
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document.write( "This is not hard to prove if you think of what you have as a base-3 number system counting from the lowest three digit combo to the highest three digit combo.\r<BR>\n" );
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