document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030400>Question 1030400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if thirteen baskets are arranged and three fruits of different types are put in each basket,,,,, in each basket a fruit is picked randomly, find the possible solutions of the thirteen picks [fruit1-mango,fruit2-orange,fruit3-lemon].......if for instance the first solution is [1,1,1,1,1,1,1,1,1,1,1,1,1] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645253 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "if thirteen baskets are arranged and three fruits of different types are put in each basket,,,,, in each basket a fruit is picked randomly, find the possible solutions of the thirteen picks [fruit1-mango,fruit2-orange,fruit3-lemon].......if for instance the first solution is [1,1,1,1,1,1,1,1,1,1,1,1,1]<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "This is a permutation with repetitions permitted.<BR>\n" );
document.write( "The number of choices at each basket is 3.<BR>\n" );
document.write( "For the next basket, the number of choices is still three (repetitions permitted), so there are 3*3=9 choices for two baskets.<BR>\n" );
document.write( "For the third basket, the number of choices is still three, so there is a total of 3*3*3=3&sup3; choices.<BR>\n" );
document.write( "Continue this until the thirteenth basket, we will have 3<sup>13</sup>=1594323 choices, which is a little long to enumerate here.<BR>\n" );
document.write( "However, the first and last ones would look like:<BR>\n" );
document.write( "1111111111111<BR>\n" );
document.write( "1111111111112<BR>\n" );
document.write( "1111111111113<BR>\n" );
document.write( "1111111111121<BR>\n" );
document.write( "1111111111122<BR>\n" );
document.write( "1111111111123<BR>\n" );
document.write( "1111111111131<BR>\n" );
document.write( "...<BR>\n" );
document.write( "...<BR>\n" );
document.write( "3333333333331<BR>\n" );
document.write( "3333333333332<BR>\n" );
document.write( "3333333333333 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );