document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193829>Question 1193829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12 balls — 4 red, 4 white, and 4 blue.\r<BR>\n" );
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document.write( "If three balls are drawn at random out of this box one at a time without replacement, what is the probability of obtaining\r<BR>\n" );
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document.write( "3 white balls?<BR>\n" );
document.write( "Answer:  1/55<BR>\n" );
document.write( "4/12 * 3/12 * 2/10\r<BR>\n" );
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document.write( "3 balls of the same color?<BR>\n" );
document.write( "Answer: 3/55<BR>\n" );
document.write( "p{(w,w,w),(R,R,R),(B,B,B)}<BR>\n" );
document.write( "    1/55 + 1/55 + 1/55\r<BR>\n" );
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document.write( "Are my answers correct? Thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825860 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Question 1: What is the probability of getting 3 white balls?\r<BR>\n" );
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document.write( "If we select without replacement, then,<BR>\n" );
document.write( "4/12 is the probability of getting a white ball<BR>\n" );
document.write( "3/11 is the probability of getting a second white ball<BR>\n" );
document.write( "2/10 is the probability of getting a third white ball<BR>\n" );
document.write( "Each time we count down by 1 for the numerator and denominator separately.\r<BR>\n" );
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document.write( "Multiply out those fractions:<BR>\n" );
document.write( "(4/12)*(3/11)*(2/10)<BR>\n" );
document.write( "(4*3*2)/(12*11*10)<BR>\n" );
document.write( "(4*3*2)/(4*3*11*2*5)<BR>\n" );
document.write( "1/(11*5)<BR>\n" );
document.write( "<font color=red>1/55<BR>\n" );
document.write( "You have the correct answer. Nice job.</font>\r<BR>\n" );
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document.write( "Here's another way to get the answer.<BR>\n" );
document.write( "There are n = 4 white balls and we select r = 3 of them.<BR>\n" );
document.write( "Using the nCr combination formula leads to 4C3 = 4 ways to do this. In other words, there are 4 ways to not select a particularly unlucky white ball.\r<BR>\n" );
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document.write( "Now let's count the number of ways to select any 3 balls regardless of color.<BR>\n" );
document.write( "We have n = 12 of them and we select r = 3<BR>\n" );
document.write( "12 C 3 = 220 ways to pick any 3 balls<BR>\n" );
document.write( "Then notice how 4/220 = (1*4)/(55*4) = <font color=red>1/55</font>\r<BR>\n" );
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document.write( "Here's some scratch work to show how to compute 12 C 3<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "12 C 3 = (12!)/(3!*(12-3)!)<BR>\n" );
document.write( "12 C 3 = (12!)/(3!*9!)<BR>\n" );
document.write( "12 C 3 = (12*11*10*9!)/(3!*9!)<BR>\n" );
document.write( "12 C 3 = (12*11*10)/(3!)<BR>\n" );
document.write( "12 C 3 = (12*11*10)/(3*2*1)<BR>\n" );
document.write( "12 C 3 = (1320)/(6)<BR>\n" );
document.write( "12 C 3 = 220<BR>\n" );
document.write( "Use this template to compute 4C3 as well if necessary.\r<BR>\n" );
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document.write( "As you can tell or already guess, order does not matter when selecting the balls which is why the nCr formula is used (rather than the nPr one).\r<BR>\n" );
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document.write( "Question 2: What is the probability of getting 3 balls of the same color?\r<BR>\n" );
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document.write( "You are correct in thinking that 1/55 is the probability of getting all red, and also all blue. This works because we have 4 of each color. <BR>\n" );
document.write( "This leads to the <font color=red>correct answer of 3/55</font>. Once again, nice work.\r<BR>\n" );
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document.write( "Side note: I appreciate you showing your work and thought process. <BR>\n" );
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