document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168268>Question 1168268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a permutation is chosen at random, what is the probability that it begins with at least 2 A's? AAABBBCCC </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792879 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Starting with AT LEAST 2 A's means starting with 3 A's, or starting with 2 A's with some different letter third.<br><BR>\n" );
document.write( "P(AAA...) = (3/9)(2/8)(1/7) = 1/84<br><BR>\n" );
document.write( "P(AAX...) (X NOT the third A) = (3/9)(2/8)(6/7) = 6/84 = 1/14<br><BR>\n" );
document.write( "P(start with AT LEAST 2 A's) = 1/84+6/84 = 7/84 = 1/12<br><BR>\n" );
document.write( "It is faster if your thinking is \"first 2 letters A and ANY letter third\":<br><BR>\n" );
document.write( "P(AA?) = (3/9)(2/8)(7/7) = 1/12<br><BR>\n" );
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