document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=642890>Question 642890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a product code is made from 3 non-distinct letters from this set { W,Y,T,U,X,R}.\r<BR>\n" );
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document.write( "how many different codes contain exactly 1 R? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404270 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=404270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If repetition is NOT allowed (ex: RTX is allowed, but RTT is NOT allowed)\r<BR>\n" );
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document.write( "Case 1) First letter is R\r<BR>\n" );
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document.write( "There are 6 letters total. After picking R, you have 5 left. So there are 5*4 = 20 ways to arrange the remaining letters in the remaining two slots.\r<BR>\n" );
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document.write( "Case 2) Second letter is R\r<BR>\n" );
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document.write( "Same as case 1, but now the R is in the second slot instead of the first. There are still 5 letters left and 5*4 = 20 ways to arrange these 5 remaining letters in the two outer slots.\r<BR>\n" );
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document.write( "Case 3) Third letter is R\r<BR>\n" );
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document.write( "Same as case 1, but now R is in slot 3. So there are 20 ways to arrange the remaining letters.\r<BR>\n" );
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document.write( "So we have 3 cases with 20 ways each giving us 3*20 = <font color=\"red\">60</font> ways total.\r<BR>\n" );
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document.write( "OR\r<BR>\n" );
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document.write( "If repetition is allowed (ex: RTT is finally allowed), then...\r<BR>\n" );
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document.write( "You have 6 letters, but you can only have exactly one R. So once you choose that R (for say the first slot), then you have 5 letters left to choose from for the second slot. Since repetition is allowed, you also have 5 letters left to choose for the 3rd slot.\r<BR>\n" );
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document.write( "So you have 5*5 = 25 ways to choose an R for the first slot, then 2 (maybe repeating) letters for the second and third slot.\r<BR>\n" );
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document.write( "This can be generalized if R was in any slot. So there are 3 times as many ways, which means that there are 3*25 = <font color=\"red\">75</font> different ways\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "So again, if repetition is NOT allowed, then there are <font color=\"red\">60</font> ways to do this.\r<BR>\n" );
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document.write( "If repetition is allowed, then there are <font color=\"red\">75</font> ways to do this. </SPAN>\n" );
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