wordpress multiple select in theme option page - php

Question

im trying to make this work. its theme option page that list categories and allow you to do MULTIPLE select
but something is wrong and it not saving the values and in the end how can i show these selected categories in index?
here is what i found in web and sof
<?php
add_action( 'admin_init', 'theme_options_init' );
add_action( 'admin_menu', 'theme_options_add_page' );
function theme_options_init(){
register_setting( 'sample_options', 'sample_theme_options', 'theme_options_validate' );
}
function theme_options_add_page() {
add_theme_page( __( 'Theme Options', 'sampletheme' ), __( 'Theme Options', 'sampletheme' ), 'edit_theme_options', 'theme_options', 'theme_options_do_page' );
}
function theme_options_do_page() {
global $select_options, $radio_options;
if ( ! isset( $_REQUEST['settings-updated'] ) )
$_REQUEST['settings-updated'] = false;
?>
<div class="wrap">
<?php screen_icon(); echo "<h2>" . get_current_theme() . __( ' Theme Options', 'sampletheme' ) . "</h2>"; ?>
<?php if ( false !== $_REQUEST['settings-updated'] ) : ?>
<div class="updated fade"><p><strong><?php _e( 'Options saved', 'sampletheme' ); ?></strong></p></div>
<?php endif; ?>
<form method="post" action="options.php">
<?php settings_fields( 'sample_options' ); ?>
<?php $options = get_option( 'sample_theme_options' ); ?>
<select multiple="multiple" name="site_options[categorychoice][]">
<?php $option = get_option('site_options'); ?>
<?php
$args = array(
'orderby' => 'name',
'parent' => 0,
'exclude' => 1
);
$categories = get_categories( $args );
foreach ($categories as $category) { ?>
<?php $selected = in_array( $category->cat_ID, $option['categorychoice'] ) ? ' selected="selected" ' : ''; ?>
<option value="<?php echo $category->term_id; ?>" <?php echo $selected; ?> >
<?php echo $category->cat_name . ' (' . $category->category_count .')'; ?>
</option>
<?php } //endforeach ?>
</select>
<p class="submit">
<input type="submit" class="button-primary" value="<?php _e( 'Save Options', 'sampletheme' ); ?>" />
</p>
</form>
</div>
<?php
}
function theme_options_validate( $input ) {
global $select_options, $radio_options, $categories;
if ( ! array_key_exists( $input['categorychoice'], $categories ) )
$input['categorychoice'] = NULL;
return $input;
}