document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087064>Question 1087064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the probability of getting vowels in the first, third, and sixth place when all the letters of the word ORANGE are arranged in all possible ways. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701347 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pr(vowel in 1st, 3rd, and 6th place) = <BR>\n" );
document.write( "    (#ways that O,A,E can be arranged in 1st, 3rd, and 6th place)  /  (#ways of arranging letters O,R,A,N,G,E)<BR>\n" );
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document.write( "#ways of arranging letters O,R,A,N,G,E = 6!<BR>\n" );
document.write( "#ways that O,A,E can appear in 1st, 3rd, and 6th place = 3! * 3! (for each vowel arrangement, you can have the remaining 3 consonants arranged in 3! ways)\r<BR>\n" );
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document.write( "Pr(vowel in 1st, 3rd, and 6th place) = (3!*3!)/6! = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight+%281%2F20%29+ ALIGN=MIDDLE  ALT=\"+highlight+%281%2F20%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Edit 7/8/17 :  Fixed answer to account for consonant arrangement which was missing from my first answer.  Thanks mathmate. <BR>\n" );
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