document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477739>Question 477739</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, could you please advise where to start on the following question...\r<BR>\n" );
document.write( "\n" );
document.write( "How many different ways can a gardener who has five (identical) red flowers, 3 (identical) pink flowers and 2 (identical) white flowers plant all the flowers in a row?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327364 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=327364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the combination formula will give you your answer.<BR>\n" );
document.write( "you have 5 red flowers, 3 pink flowers, and 2 white flowers.<BR>\n" );
document.write( "i believe you answer will be given by the following formula:<BR>\n" );
document.write( "number of possible combination is equal to:<BR>\n" );
document.write( "n!/(x!*y!*z!)<BR>\n" );
document.write( "n is the total number of flowers<BR>\n" );
document.write( "x is the number of red flowers<BR>\n" );
document.write( "y is the number of pink flowers<BR>\n" );
document.write( "z is the number of white flowers<BR>\n" );
document.write( "the actual numbers replace the letters to get:<BR>\n" );
document.write( "10!/(5!*3!*2!) which is equal to 2520 possible arrangements.<BR>\n" );
document.write( "this is hard to see because there are so many combinations.<BR>\n" );
document.write( "it's easier to see when there are fewer.<BR>\n" );
document.write( "assume you had 5 flowers in total.<BR>\n" );
document.write( "2 are red and 3 are blue<BR>\n" );
document.write( "the number of ways you can arrange them should be 5!/(2!*3!) = 10<BR>\n" );
document.write( "if we let a equal to the red flowers and b equal the blue flowers, then we can model the arrangements are shown below:<BR>\n" );
document.write( "aa is in the first 2 positions<BR>\n" );
document.write( "aabbb<BR>\n" );
document.write( "ab is in the first 2 positions<BR>\n" );
document.write( "ababb<BR>\n" );
document.write( "abbab<BR>\n" );
document.write( "abbba<BR>\n" );
document.write( "ba is in the first 2 positions<BR>\n" );
document.write( "baabb<BR>\n" );
document.write( "babab<BR>\n" );
document.write( "babba<BR>\n" );
document.write( "bb is in the first 2 positions<BR>\n" );
document.write( "bbaab<BR>\n" );
document.write( "bbaba<BR>\n" );
document.write( "bbbaa<BR>\n" );
document.write( "total possible combinations is 10.<BR>\n" );
document.write( "same concept works with the bigger numbers.<BR>\n" );
document.write( "10! / (5!*3!*2!) = 2520 possible arrangements. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );