Count of posts by different parameters?

Use WP_Query with a tax_query and a meta_query argument, and return only IDs to save a bit of server resource.

$args = array(
  'post_type' => 'post',
  'tax_query' => array(
    array(
      'taxonomy' => 'people',
      'field'    => 'slug',
      'terms'    => 'bob',
    ),
  ),
  'meta_query' => array(
    array(
      'key'     => 'age',
      'value'   => array( 3, 4 ),
      'compare' => 'IN',
    ),
  ),
  'fields' => 'ids'.
);
$query = new WP_Query( $args );

And check the found_posts element of $query— var_dump($query->found_posts);