document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184465>Question 1184465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box contains 20 balls out which 7 are white balls, 5 are black balls, 6 are<BR>\n" );
document.write( "red balls and 2 are yellow balls. If four balls are drawn at random. What is<BR>\n" );
document.write( "the probability that balls of one colour, balls of two colours and balls of three colours are drawn? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815105 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 20C4 ways to draw 4 balls=4845<BR>\n" );
document.write( "one color<BR>\n" );
document.write( "white is 7C4/20C4=35/4845 and may be reduced.<BR>\n" );
document.write( "black is 5C4/20C4=5/4845<BR>\n" );
document.write( "red is 6C4/20C4=15/4845<BR>\n" );
document.write( "yellow is 0 since there must be at least 4 of them.<BR>\n" );
document.write( "balls of 1 color has probability of 55/4845 of being drawn<BR>\n" );
document.write( "--<BR>\n" );
document.write( "two colors would be <BR>\n" );
document.write( "(same denominator or 4845)<BR>\n" );
document.write( "white black<BR>\n" );
document.write( "7C1*5C3+7C2*5C2+7C3*5C1=70+210=175=455<BR>\n" );
document.write( "-<BR>\n" );
document.write( "white red<BR>\n" );
document.write( "7C1*6C3+7C2+6C2+7C3*6C1=140+315+210=665<BR>\n" );
document.write( "-<BR>\n" );
document.write( "white-yellow<BR>\n" );
document.write( "7C2*2C2+7C3+2C1=21+70=91<BR>\n" );
document.write( "-<BR>\n" );
document.write( "black-red <BR>\n" );
document.write( "5C1*6C3+5C2*6C2+5C3*6C1=100+150+60=310<BR>\n" );
document.write( "-<BR>\n" );
document.write( "black-yellow<BR>\n" );
document.write( "5C2*2C2+5C3*2C1=30<BR>\n" );
document.write( "-<BR>\n" );
document.write( "red-yellow<BR>\n" );
document.write( "6C2*2C2+6C3*2C1=55<BR>\n" );
document.write( "Total for these is 1606/4845<BR>\n" );
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document.write( "w-b-r<BR>\n" );
document.write( "7C2*5C1*6C1+7C1*5C2*6C1+7C1*5C1*6C2=630+420+525=1575<BR>\n" );
document.write( "w-b-y<BR>\n" );
document.write( "7C2*5C1*2C1+7C1*5C2*2C1+7C1*5C1*2C2=210+140+35=385<BR>\n" );
document.write( "-<BR>\n" );
document.write( "w-r-y<BR>\n" );
document.write( "7C2*6C1*2C1+7C1*6C2*2C1+7C1*6C1*2C2=252+210+42=504<BR>\n" );
document.write( "-<BR>\n" );
document.write( "b-r-y<BR>\n" );
document.write( "5C2*6C1*2C1+5C1*6C2*2C1+5C1*6C1*2C2=120+150+30=300<BR>\n" );
document.write( "That total is 2764/4845<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Not asked for but balls of 4 colors would be 7C2*5C1*6C1*2C1=420/4845\r<BR>\n" );
document.write( "\n" );
document.write( "55+1606+2764+420=4845, and that accounts for all the possibilities.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );