# NAME

Math::Counting - Combinatorial counting operations

version 0.1307

# SYNOPSIS

``````  use Math::Counting ':student';
printf "Given n=%d, k=%d:\nF=%d\nP=%d\nC=%d\n",
\$n, \$k, factorial(\$n), permutation(\$n, \$k), combination(\$n, \$k);``````

Engineering

``````  use Math::Counting ':big';
printf "Given n=%d, k=%d, r=%d:\nF=%d\nP=%d\nD=%d\nC=%d\n",
\$n, \$k, \$r, bfact(\$n), bperm(\$n, \$k, \$r), bderange(\$n), bcomb(\$n, \$k, \$r);``````

# DESCRIPTION

Compute the factorial, number of permutations, number of derangements and number of combinations.

The `:big` functions are wrappers around "bfac" in Math::BigInt with a bit of arithmetic between.

The student versions exist to illustrate the computation "in the raw" as it were. To see these computations in action, Use The Source, Luke.

# FUNCTIONS

## factorial

``  \$f = factorial(\$n);``

Return the number of arrangements of n, notated as `n!`.

This function employs the algorithmically elegant "student" version using real arithmetic.

## bfact

``  \$f = bfact(\$n);``

Return the value of the function "bfac" in Math::BigInt, which is the "Right Way To Do It."

## permutation

``  \$p = permutation(\$n, \$k);``

Return the number of arrangements, without repetition, of k elements drawn from a set of n elements, using the "student" version.

## bperm

``  \$p = bperm(\$n, \$k, \$r);``

Return the computations:

``````  n^k           # with repetition \$r == 1
n! / (n-k)!   # without repetition \$r == 0``````

## bderange()

"A derangement is a permutation in which none of the objects appear in their "natural" (i.e., ordered) place." -- wolfram under "SEE ALSO"

Return the computation:

``  !n = n! * ( sum (-1)^k/k! for k=0 to n )``

## combination

``  \$c = combination(\$n, \$k);``

Return the number of ways to choose k elements from a set of n elements, without repetition.

This is algorithm expresses the "student" version.

## bcomb

``  \$c = bcomb(\$n, \$k, \$r);``

Return the combination computations:

``````  (n+k-1)! / k!(n-1)!   # with repetition \$r == 1
n! / k!(n-k)!         # without repetition \$r == 0``````

# TO DO

Provide the gamma function for the factorial of non-integer numbers?

"bfac" in Math::BigInt

Math::BigFloat

Higher Order Perl by Mark Jason Dominus (http://hop.perl.plover.com).

Mastering Algorithms with Perl by Orwant, Hietaniemi & Macdonald (http://www.oreilly.com/catalog/maperl).

http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html

http://mathworld.wolfram.com/Derangement.html

Naturally, there are a plethora of combinatorics packages available, take your pick:

# CREDITS

Special thanks to:

* Paul Evans

* Mike Pomraning

* Petar Kaleychev

* Dana Jacobsen

# AUTHOR

Gene Boggs <gene@cpan.org>