n!/4!(n-2)! =3
\n" );
document.write( "\r\n" );
document.write( "I'll say this mainly for Ikleyn's benefit. Yours too if you're tuned in\r\n" );
document.write( "MathTherapy. Students almost never have to write algebra all on one line\r\n" );
document.write( "anymore, EXCEPT ON THIS SITE! and most of them do not understand Igor's \"formula\r\n" );
document.write( "notation\" program, which I use extensively. Thus I forgive them for a certain\r\n" );
document.write( "implication of the order of operations never having dawned upon them, for I'm\r\n" );
document.write( "sure that their teachers have never brought it up to them. That is, if a\r\n" );
document.write( "numerator or denominator contains more than one term, or has more than one\r\n" );
document.write( "factor showing, then the entire numerator or denominator must go inside\r\n" );
document.write( "parentheses. Incidentally, even Igor's \"formula notation\" contains a\r\n" );
document.write( "flaw, for it falsely assumes\r\n" );
document.write( "\r\n" );
document.write( "a/bc, typed with three \"{\"'s before it and three \"}\"'s after it, means this\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "when it actually means this: \r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "I wrote Igor about this years ago, but he seemed to think I was wrong, and \r\n" );
document.write( "never fixed it. I didn't want to have an argument, so I've just lived with it. \r\n" );
document.write( "\r\n" );
document.write( "Anyway I always assume parentheses around a numerator or denominator were meant\r\n" );
document.write( "when it would change the meaning to something more likely to be what the student\r\n" );
document.write( "meant. So I assume this problem should be:\r\n" );
document.write( "\r\n" );
document.write( "n!/(4!(n-2)!) = 3\r\n" );
document.write( "\r\n" );
document.write( "and I forgive this student for not putting parentheses around the denominator he\r\n" );
document.write( "meant:\r\n" );
document.write( "\r\n" );
document.write( "I am pretty sure this student meant this:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Thus,\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by the denominator on the left:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "We disregard the negative answer, since factorials are\r\n" );
document.write( "only defined for non-negative integers. So,\r\n" );
document.write( "\r\n" );
document.write( "answer = 9 is correct.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "