Solver Permutations and Combinations (with NPR and NCR)

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(28504)

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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