<footer>

  <div class='footer-tags'>
    <h3>Random Tags</h3>
    <ol>
      <% blog.tags.to_a.shuffle[0...10].each do |tag, articles| %>
        <li><%= link_to "#{tag}", tag_path(tag) %></li>
      <% end %>
    </ol>
  </div>

  <div class='recent-posts'>
    <h3>Random Posts</h3>
    <ol>
      <% blog.articles.shuffle[0...10].each do |article| %>
        <li><%= link_to article.title, article %></li>
      <% end %>
    </ol>
  </div>

</footer>

<footer>

  <div class='footer-tags'>
    <h3>Random Tags</h3>
    <ul class='random-tag-list'>
      <% blog.tags.to_a.shuffle[0...10].each do |tag, articles| %>
        <li><%= link_to "#{tag}", tag_path(tag) %></li>
      <% end %>
    </ul>
  </div>

  <div class='recent-posts'>
    <h3>Random Posts</h3>
    <ul>
      <% blog.articles.shuffle[0...10].each do |article| %>
        <li><%= link_to article.title, article %></li>
      <% end %>
    </ul>
  </div>

</footer>

Change lists from ol to ul tags
Change lists from ol to ul tags
