document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477545>Question 477545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear math teacher, <BR>\n" );
document.write( "I am having the following difficulties with this problem: <BR>\n" );
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?\" <BR>\n" );
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. <BR>\n" );
document.write( "Here is what I did by Method 1 for part a): <BR>\n" );
document.write( "R W B<BR>\n" );
document.write( "n 7 6 4<BR>\n" );
document.write( "r 3 <BR>\n" );
document.write( "7C3 = 35 selections <BR>\n" );
document.write( "Here is what I did by Method 1 for part b): <BR>\n" );
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. <BR>\n" );
document.write( "Method 2 part b) <BR>\n" );
document.write( "n (total R, W, B) = 7+6+4 = 17<BR>\n" );
document.write( "r = 3 <BR>\n" );
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? <BR>\n" );
document.write( "Thank you very much for your help. <BR>\n" );
document.write( "Respectfully, \r<BR>\n" );
document.write( "\n" );
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 #327316 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=327316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the two groups are \"all red cards\" and \"no red cards\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in method 2 you found all possible ways to select 3 cards; and then subtracted all the ways to get 3 red cards<BR>\n" );
document.write( "___ this does not account for groups containing one or two red cards </SPAN>\n" );
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