Solver Permutations and Combinations (with NPR and NCR)

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Source code of 'Permutations and Combinations (with NPR and NCR)'

This Solver (Permutations and Combinations (with NPR and NCR)) was created by by jim_thompson5910(13794)

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==section input
Enter whole number values for n and r (where n goes in the first box and r goes in the second one) and choose between {{{nPr}}} or {{{nCr}}} to calculate the permutation or combination

*[input n=5] *[choice path NPR NCR] *[input r=5]

==section solution

perl

sub CommaFormatted
{
	my $delimiter = ','; # replace comma if desired
	my($n,$d) = split /\./,shift,2;
	my @a = ();
	while($n =~ /\d\d\d\d/)
	{
		$n =~ s/(\d\d\d)$//;
		unshift @a,$1;
	}
	unshift @a,$n;
	$n = join $delimiter,@a;
	$n = "$n\.$d" if $d =~ /\d/;
	return $n;
}

sub fac {
  my ($n) = @_;

if($n==0)
  { return 1;}

if ($n < 2) {
    return $n;
  }
  else {
    return $n * fac($n-1);
  }
}

$npr=fac($n)/(fac($n-$r));
$ncr=fac($n)/(fac($n-$r)*fac($r));

$result=fac($n);

if($n<$r)
{print "The value of n must be greater than r.";
return undef;}

if(($n=~m/\D/)||($r=~m/\D/))
{print "You must enter whole numbers only.";
return undef;}

if($result=~m/e\+(\d+)/)
{$ee=$1;}

$ee=~s/^0//;

if($n>150)
{print "Overflow: $n is way too large";
return undef;}

if($n>17)
{print "Sorry the computer cannot accurately calculate and display $n! (the resulting factorial has $ee digits!)";
return undef;}

## NPR

if($path eq NPR)
{
print "Start with the given expression

\*\[Tex \\LARGE \\textrm{_{n}P_{r}=\\frac{n!}{(n-r)!}}]

\*\[Tex \\LARGE \\textrm{_{$n}P_{$r}=\\frac{$n!}{($n-$r)!}}] Plug in {{{n=$n}}} and {{{r=$r}}}

\*\[Tex \\LARGE \\textrm{_{$n}P_{$r}=\\frac{$n!}{",$n-$r,"!}}] Subtract {{{$n-$r}}} to get ",$n-$r,"

\*\[Tex \\LARGE \\textrm{_{$n}P_{$r}=\\frac{",fac($n),"}{",$n-$r,"!}}] Calculate $n! to get ",CommaFormatted(fac($n))," (note: if you need help with factorials, check out this <a href=http://www.algebra.com/algebra/homework/Probability-and-statistics/factorial.solver>solver</a>)

\*\[Tex \\LARGE \\textrm{_{$n}P_{$r}=\\frac{",fac($n),"}{",fac($n-$r),"}}] Calculate ",$n-$r,"! to get ",CommaFormatted(fac($n-$r)),"

\*\[Tex \\LARGE \\textrm{_{$n}P_{$r}=",fac($n)/fac($n-$r),"] Divide ",CommaFormatted(fac($n))," by ",CommaFormatted(fac($n-$r))," to get ",CommaFormatted(fac($n)/(fac($n-$r))),"

So $n choose $r (where order does matter) yields ",CommaFormatted(fac($n)/(fac($n-$r)))," unique combination", ($npr>1)?"s":"

}

## END NPR

## NCR

if($path eq NCR)
{
print "Start with the given expression

\*\[Tex \\LARGE \\textrm{_{n}C_{r}=\\frac{n!}{(n-r)!r!}}]

\*\[Tex \\LARGE \\textrm{_{$n}C_{$r}=\\frac{$n!}{($n-$r)!$r!}}] Plug in {{{n=$n}}} and {{{r=$r}}}

\*\[Tex \\LARGE \\textrm{_{$n}C_{$r}=\\frac{$n!}{",$n-$r,"!$r!}}] Subtract {{{$n-$r}}} to get ",$n-$r,"

\*\[Tex \\LARGE \\textrm{_{$n}C_{$r}=\\frac{",fac($n),"}{",$n-$r,"!$r!}}] Calculate $n! to get ",CommaFormatted(fac($n))," (note: if you need help with factorials, check out this <a href=http://www.algebra.com/algebra/homework/Probability-and-statistics/factorial.solver>solver</a>)

\*\[Tex \\LARGE \\textrm{_{$n}C_{$r}=\\frac{",fac($n),"}{(",fac($n-$r),")($r!)}}] Calculate ",$n-$r,"! to get ",CommaFormatted(fac($n-$r)),"

\*\[Tex \\LARGE \\textrm{_{$n}C_{$r}=\\frac{",fac($n),"}{(",fac($n-$r),")(",fac($r),")}}] Calculate ",$r,"! to get ",CommaFormatted(fac($r)),"

\*\[Tex \\LARGE \\textrm{_{$n}C_{$r}=\\frac{",fac($n),"}{",fac($n-$r)*fac($r),"}}] Multiply the values ",CommaFormatted(fac($n-$r))," and ",CommaFormatted(fac($r))," to get ",CommaFormatted(fac($n-$r)*fac($r)),"

\*\[Tex \\LARGE \\textrm{_{$n}C_{$r}=",fac($n)/(fac($n-$r)*fac($r)),"] Divide ",CommaFormatted(fac($n))," by ",CommaFormatted(fac($n-$r)*fac($r))," to get ",CommaFormatted(fac($n)/(fac($n-$r)*fac($r))),"

So $n choose $r (where order does not matter) yields ",CommaFormatted(fac($n)/(fac($n-$r)*fac($r)))," unique combination", ($ncr>1)?"s":"

}

## END NCR

==section output

==section check
  angle=40 angle1=50