document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=306204>Question 306204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. A bag contains two red balls, three blue balls and five green balls. Three balls are drawn at random. Find the probability that <BR>\n" );
document.write( "a) the three balls are of different colours.  <BR>\n" );
document.write( "b) two balls are of the same colour.<BR>\n" );
document.write( "c) all the three are of the same colour.                                                           10 marks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #219167 by </B><A HREF=/tutors/aboutme.mpl?userid=toidayma><B>toidayma(44)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=toidayma><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=toidayma><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=219167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let nCk = number of ways to pick up k items from a set of n items.<BR>\n" );
document.write( "Of course you should already know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nCk+=+n%21%2F%28k%21%2A%28n-k%29%21%29 ALIGN=MIDDLE  ALT=\"nCk+=+n%21%2F%28k%21%2A%28n-k%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (*)<BR>\n" );
document.write( "Bag consists of 2 red balls (R), 3 blue balls (B) and 5 green balls (G)<BR>\n" );
document.write( "How many ways to pick up any 3 balls from the bag: 10C3 <BR>\n" );
document.write( "a> three drawn balls are of different colors --> this means to pick 1R, 1B and 1G<BR>\n" );
document.write( "--> there are totally of 2C1*3C1*5C1 --> probability of 2C1*3C1*5C1/10C3<BR>\n" );
document.write( "b> two of three drawn balls are of the same color.<BR>\n" );
document.write( "There are 3 cases: the two balls of same color are red(1), blue (2) and green(3).<BR>\n" );
document.write( "(1) means 2R and any one out of the 8 other balls (3B and 5G) --> 2C2*8C1<BR>\n" );
document.write( "(2) means 2B and any one out of the 7 other balls (2R and 5G) --> 3C2*7C1<BR>\n" );
document.write( "(3) means 2G and any one out of the 5 other balls (2R and 3B) --> 5C2*5C1<BR>\n" );
document.write( "Thus, there are totally 2C2*8C1 + 3C2*7C1 + 5C2*5C1 ways to pick out 3 balls, 2 of which are of the same color --> the probability of (2C2*8C1 + 3C2*7C1 + 5C2*5C1)/10C3<BR>\n" );
document.write( "c> all the three balls are of the same color.<BR>\n" );
document.write( "This one is a bit more interesting. Obviously, the three drawn balls can't be red since there are only 2 red balls. Thus, there are only 2 cases: all three balls of the same color are blue(4) and green(5)<BR>\n" );
document.write( "(4) means to pick 3B out of the 3 blue balls --> 3C3<BR>\n" );
document.write( "(5) means to pick 3G out of the 5 green balls --> 5C3<BR>\n" );
document.write( "Thus, there are totally 3C3 + 5C3 ways to pick out 3 balls, 2 of which are of the same color --> the probability of (3C3 + 5C3)/10C3<BR>\n" );
document.write( "You surely can use the (*) for the final calculations, right? </SPAN>\n" );
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