I"m writing a series of probability problems and would like to use the n choose k function C(n,k) but I get an error. the problem works if I use the factorial n!, k! etc.

can I use Cn,k) in this case?

DOCUMENT();

loadMacros(

"PGstandard.pl", # Standard macros for PG language

"MathObjects.pl",

#"source.pl", # allows code to be displayed on certain sites.

"PGcourse.pl", # Customization file for the course

"parserPopUp.pl",

"AnswerFormatHelp.pl",

"PGauxiliaryFunctions.pl",

);

# sampling rate problem with aliasing

TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect

$showPartialCorrectAnswers = 1;

##############################################################

#

# Setup

#

#

Context("Numeric");

Context()->variables->are(m=>'Real',n=>'Real',k=>'Real');

#$test = Formula("1-C(k,n)/C(k,m+n)");

#$test = Formula("(fact(n)/(fact(n-k)*fact(k))");

$test = Formula("1-(n!/((n-k)!*k!))/((m+n)!/((m+n-k)!*k!))")->reduce;

$test->{test_points} = [[4,3,1],[5,4,3],[6,4,3]]; # remember set all 3 variables

##############################################################

#

# Text

#

#

Context()->texStrings;

BEGIN_TEXT

This problem is related to ECE514, HW1 Problem 4.

$PAR

There are \(m\) white balls and \(n\) black balls in a box. We draw \(k\) balls from the box. What is the probability of drawing at least one white ball?

$BR

P(at least one white ball) = \{ans_rule(40)\} \{ AnswerFormatHelp("formulas") \}

END_TEXT

Context()->normalStrings;

##############################################################

#

# Answers

#

#

ANS($test->cmp());

loadMacros(

"PGstandard.pl", # Standard macros for PG language

"MathObjects.pl",

#"source.pl", # allows code to be displayed on certain sites.

"PGcourse.pl", # Customization file for the course

"parserPopUp.pl",

"AnswerFormatHelp.pl",

"PGauxiliaryFunctions.pl",

);

# sampling rate problem with aliasing

TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect

$showPartialCorrectAnswers = 1;

##############################################################

#

# Setup

#

#

Context("Numeric");

Context()->variables->are(m=>'Real',n=>'Real',k=>'Real');

#$test = Formula("1-C(k,n)/C(k,m+n)");

#$test = Formula("(fact(n)/(fact(n-k)*fact(k))");

$test = Formula("1-(n!/((n-k)!*k!))/((m+n)!/((m+n-k)!*k!))")->reduce;

$test->{test_points} = [[4,3,1],[5,4,3],[6,4,3]]; # remember set all 3 variables

##############################################################

#

# Text

#

#

Context()->texStrings;

BEGIN_TEXT

This problem is related to ECE514, HW1 Problem 4.

$PAR

There are \(m\) white balls and \(n\) black balls in a box. We draw \(k\) balls from the box. What is the probability of drawing at least one white ball?

$BR

P(at least one white ball) = \{ans_rule(40)\} \{ AnswerFormatHelp("formulas") \}

END_TEXT

Context()->normalStrings;

##############################################################

#

# Answers

#

#

ANS($test->cmp());