##DESCRIPTION
##   Simplify 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"
);

TEXT(&beginproblem);

#
# Choose the denominator
#

$b = random(1,30);

#Pick how many more the numerator will be
$c = random(1,5);

#Calculate the numerator
$a = $b + $c;

#calculate the answer
$ans = $a;
for($j=$b+1; $j<$a; $j++) {
  $ans *= $j;
}

#Now the problem


BEGIN_TEXT
Evaluate \[\frac{$a !}{$b !}\]
	$PAR
	\(\frac{$a !}{$b !}\) =\{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(num_cmp($ans));

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