Category Post Count

Use get_categories–in this case for category 3

<?php
$args=array(
  'include' => 3,
  'orderby' => 'name',
  'order' => 'ASC'
  );
$categories=get_categories($args);
  foreach($categories as $category) {
    echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name . ' with '  . $category->count . ' posts </a> </p> ';
  }
?>

See Function_Reference/get_categories for more arguments

$catid = get_cat_ID('your category name here');
$args=array(
  'include' => $catid,
  'orderby' => 'name',
  'order' => 'ASC'
  );

That link above would have told you about hide_empty

$args=array(
  'hide_empty' => 0,
  'include' => $catid,
  'orderby' => 'name',
  'order' => 'ASC'
  );