##DESCRIPTION
##   Simplifying factorials
##ENDDESCRIPTION

## KEYWORDS('Sequences and Series')
## Tagged by ynw2d

## DBsubject('Algebra')
## DBchapter('Sequences and Series')
## DBsection('Arithmetic Sequences')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
##KEYWORDS('algebra', 'sequence')

##KEYWORDS('factorials')

#
# First comes some stuff that appears at the beginning of every problem
#

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"PGasu.pl",
"extraAnswerEvaluators.pl"
);

TEXT(&beginproblem);

#
# Now we do the randomization of variables, and other computations
# as needed for this problem.  Sometimes we compute the answers here.
#

#pick the coefficient for n
$a = random(2,4);

#pick the number to add to the numerator
$b = random(1,4);

#pick the number to add to the denominator
$c = random (1,3);

#this will compute the answer to the problem
#set the answer to the first possible term
$ans = "($a*n-$c+1)";
#concatenate the rest of the terms up to $b

for($j=-$c+2;$j<=$b;$j++){$ans.="*($a*n+$j)";}


#
# Now the problem text itself, with ans_rule's to indicate where the
# answers go.  You can stop entering text, do more computations, and then
# start up again if you want.
#

BEGIN_TEXT
Simplify the expression \[\frac{($a n + $b)!}{($a n - $c)!}\].
	$PAR
	\(\frac{($a n + $b)!}{($a n - $c)!}\)= \{ans_rule(40)\}
END_TEXT

#
# Tell WeBWork how to test if answers are right.  These should come in the
# same order as the answer blanks above.  You tell WeBWork both the type of
# "answer evaluator" to use, and the correct answer.
#

&ANS(fun_cmp($ans, var => 'n'));

ENDDOCUMENT();        # This should be the last executable line in the problem.