Show all categories and their posts?

<?php
//for each category, show 3 posts
$cat_args=array(
  'orderby' => 'name',
  'order' => 'ASC'
   );
$categories=get_categories($cat_args);
  foreach($categories as $category) {
    $args=array(
      'showposts' => 3,
      'category__in' => array($category->term_id),
      'caller_get_posts'=>1
    );
    $posts=get_posts($args);
      if ($posts) {
        echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
        foreach($posts as $post) {
          setup_postdata($post); ?>
          <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
          <?php
        } // foreach($posts
      } // if ($posts
    } // foreach($categories
?>

Didn’t seem to work. I’m messing it up no doubt. Which template should this go into? Anything special I need to do with the loop? Sorry, newb..

For examle, this works just fine for me with the WordPress Default theme’s wp-content/themes/default/index.php and placed just before:

<?php if (have_posts()) : ?>

Ah! It worked. I’m learning this while trying to develop a custom theme. Can I adjust the showposts value to show all posts in the category?

i want to show latest post with content of each category.

what changes should i make in above code to work.