document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477438>Question 477438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear math teacher, \r<BR>\n" );
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document.write( "I am having the following difficulties with this problem: \r<BR>\n" );
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document.write( "\"A box contains 7 red cards, 6 white cards and 4 blue cards.  How many selections of three cards can be made so that a) all three are red, b) none are red?\" \r<BR>\n" );
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document.write( "I solved the problem correctly but then I tried to solve it the second way - the shorter and less time consuming way.  I was supposed to get the same result but did not.  Please let me know, why I did not get the same answer. \r<BR>\n" );
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document.write( "Here is what I did by Method 1 for part a): \r<BR>\n" );
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document.write( "     R     W      B<BR>\n" );
document.write( "n    7     6      4<BR>\n" );
document.write( "r    3\r<BR>\n" );
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document.write( "7C3 = 35 selections\r<BR>\n" );
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document.write( "Here is what I did by Method 1 for part b): \r<BR>\n" );
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document.write( "     R    W      B<BR>\n" );
document.write( "n    7    6      4<BR>\n" );
document.write( "r                      n = 6+4 = 10<BR>\n" );
document.write( "                       r = 3<BR>\n" );
document.write( "10C3 = 10!/(10-3)! = 120 selections. \r<BR>\n" );
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document.write( "Method 2 part b)\r<BR>\n" );
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document.write( "n (total R, W, B) = 7+6+4 = 17<BR>\n" );
document.write( "r = 3\r<BR>\n" );
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document.write( "17C3 - 7C3 = 680-35 =  645 selections and this answer does not match the answer obtained by Method 1 for part b). Would you tell me why?  Where did I do a mistep? Here is how reasoned it out: Total Number of Ways - Number of Ways to Pull Red Cards = Number of Ways to Get Other Colors<BR>\n" );
document.write( "Why would that be wrong to think like that?\r<BR>\n" );
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document.write( "Thank you very much for your help.  \r<BR>\n" );
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document.write( "Respectfully, \r<BR>\n" );
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document.write( "Ivanka </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327238 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=327238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"A box contains 7 red cards, 6 white cards and 4 blue cards. How many selections of three cards can be made so that <BR>\n" );
document.write( "a) all three are red, <BR>\n" );
document.write( "Easiest Way:<BR>\n" );
document.write( "# of ways to get 3 red: 7C3 = (7*6*5)/(1*2*3) = 35<BR>\n" );
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document.write( "b) none are red?<BR>\n" );
document.write( "Easiest Way:<BR>\n" );
document.write( "# of ways to get 3 not red: 10C3 = (10*9*8)/(1*2*3) = 120<BR>\n" );
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document.write( "Your Question::::::<BR>\n" );
document.write( "17C3 - 7C3 = 680-35 = 645 <BR>\n" );
document.write( "The 645 includes all the combinations that allow<BR>\n" );
document.write( "1 red in the group of 3 or 2 reds in the group of 3.<BR>\n" );
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document.write( "Your 35 is the # of groups with ALL red<BR>\n" );
document.write( "Your 120 is the # of groups with NO red<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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