document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=863759>Question 863759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are nine balls in a basket. Three of these balls are blue, three are red, and three are green. A boy randomly picks three balls from the basket.\r<BR>\n" );
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document.write( "How many possible combinations of balls are there? \r<BR>\n" );
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document.write( "(I did this question and got the right answer just by brute force counting, but I want to know if there is a way to do this question using proper math. The possible combinations are (B- Blue, R- Red, G- Green): \r<BR>\n" );
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document.write( "B-B-B<BR>\n" );
document.write( "B-B-R<BR>\n" );
document.write( "B-R-R<BR>\n" );
document.write( "R-R-R<BR>\n" );
document.write( "R-R-G<BR>\n" );
document.write( "R-G-G<BR>\n" );
document.write( "G-G-G<BR>\n" );
document.write( "G-G-B<BR>\n" );
document.write( "G-B-B<BR>\n" );
document.write( "B-R-G\r<BR>\n" );
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document.write( "For a total of ten possible combinations.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520594 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=520594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For each choice you can pick 1 of 3 balls.<BR>\n" );
document.write( "You have 3 choices to make so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=3%2A3%2A3=27 ALIGN=MIDDLE  ALT=\"N=3%2A3%2A3=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Easiest way to count is to make a chart with 3 columns.<BR>\n" );
document.write( "In the 3rd column, place B,R,G alternately for 27 entries.<BR>\n" );
document.write( "In the 2nd column, place B for 3 rows, R for 3 rows, G for 3 rows, then repeat.<BR>\n" );
document.write( "In the 1st column, place B for 9 rows, R for 9 rows, G for 9 rows. <BR>\n" );
document.write( "That will get you all the values. \r<BR>\n" );
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document.write( "BBB <BR>\n" );
document.write( "BBR <BR>\n" );
document.write( "BBG <BR>\n" );
document.write( "BRB <BR>\n" );
document.write( "BRR <BR>\n" );
document.write( "BRG <BR>\n" );
document.write( "BGB <BR>\n" );
document.write( "BGR <BR>\n" );
document.write( "BGG<BR>\n" );
document.write( "RBB <BR>\n" );
document.write( "RBR <BR>\n" );
document.write( "RBG <BR>\n" );
document.write( "RRB <BR>\n" );
document.write( "RRR <BR>\n" );
document.write( "RRG <BR>\n" );
document.write( "RGB <BR>\n" );
document.write( "RGR <BR>\n" );
document.write( "RGG<BR>\n" );
document.write( "GBB <BR>\n" );
document.write( "GBR <BR>\n" );
document.write( "GBG <BR>\n" );
document.write( "GRB <BR>\n" );
document.write( "GRR <BR>\n" );
document.write( "GRG <BR>\n" );
document.write( "GGB <BR>\n" );
document.write( "GGR <BR>\n" );
document.write( "GGG </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );