<?php
$terms = get_terms( array(
'taxonomy' => 'category',
'parent' => '10'
) );
if ( !empty( $terms ) && !is_wp_error( $terms ) ){
echo '<ul>';
foreach ( $terms as $term ) {
echo '<li>' . $term->name . ' (' . $term->count . ')' . '</li>';
}
echo '</ul>';
}
?>