.. _sphx_glr_api_gallery_combinatorics_counting:

Counting
----------

Permutation/combination counting and generation, and multinomial
coefficients.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Counts 5-card poker hands and a few hand types, and cross-checks the count against brute-force enumeration for a smaller deck.">

.. only:: html

  .. image:: /api/gallery/combinatorics/counting/images/thumb/sphx_glr_plot_01_poker_hands_thumb.png
    :alt:

  :doc:`/api/gallery/combinatorics/counting/plot_01_poker_hands`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Counting poker hands</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Levi ben Gershon&#x27;s 1321 Maaseh Hoshev proved by induction that n objects can be arranged in n! orders, that k of them can be arranged in n!/(n-k)! ways, and that k can be chosen in n!/(k!(n-k)!) ways. This example checks each formula against brute-force enumeration.">

.. only:: html

  .. image:: /api/gallery/combinatorics/counting/images/thumb/sphx_glr_plot_02_gersonides_formulas_thumb.png
    :alt:

  :doc:`/api/gallery/combinatorics/counting/plot_02_gersonides_formulas`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gersonides' counting formulas</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/combinatorics/counting/plot_01_poker_hands
   /api/gallery/combinatorics/counting/plot_02_gersonides_formulas