Pull random image from entries marked with a certain category
Welcome to the Craft community @bjyama

{# Step one: pick a random service #}
{% set randomService = craft.entries.section('services').relatedTo(left).order('RAND()').first() %}

{# Step two: pick a random image from the above service #}
{% set randomServiceImage = service.homepageImage.order('RAND()').first() %}

{% if randomServiceImage %}
    &lt;img src="{{ randomServiceImage.getUrl('imageTransformName') }}" alt=""&gt;
{% endif %}


For more info, have a look here: https://craftcms.com/docs/templating/craft.entries#order

Let us know how you get on :)