document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=467690>Question 467690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many ways can you arrange A-F with a consonant at one end, and a vowel at the other?\r<BR>\n" );
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document.write( "we answered other similiar problems using factorials  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320925 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=320925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **For any set of n objects, there are n! ways of arranging them**<BR>\n" );
document.write( "Now for the letters A-F, there are 2 vowels and 4 consonants <BR>\n" );
document.write( "If a vowel is at one end and a consonant at the other then that leaves 4 letters remaining to be arranged in any which way between them.<BR>\n" );
document.write( "From above we know then that are 4! ways of arranging 4 letters.<BR>\n" );
document.write( "Say the consonant B is on the front end and a vowel on other end:<BR>\n" );
document.write( "B _ _ _ _ Vowel<BR>\n" );
document.write( "There are only 2 possibilities because there are only 2 vowels to choose from:<BR>\n" );
document.write( "B _ _ _ _ A     OR   B _ _ _ _ E<BR>\n" );
document.write( "Each of these has 4! arrangements<BR>\n" );
document.write( "So with B at the front there are 2*(4!) arrangements<BR>\n" );
document.write( "However, there are 4 consonants each of which could be at the front end<BR>\n" );
document.write( "So multiply by 4<BR>\n" );
document.write( "With any consonant at front end there are 4*2*(4!) arrangements<BR>\n" );
document.write( "However, the consonant could also be at back end with vowel in front<BR>\n" );
document.write( "Since everything else would stay the same, double the possible arrangements<BR>\n" );
document.write( "Total number of arrangements are 2*4*2*(4!) arrangements which simplifies to 16(4!) </SPAN>\n" );
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