WooCommerce: Get newest products and sort them (partially) randomly

I want to get the last 20 posts (in my case WooCommerce products) and show 10 of them in a random order.

For now I get the new posts like this:

$args = array(
    'post_type'                     => 'product',
    'orderby'                       => 'date',
    'order'                         => 'DESC',
    'posts_per_page'                => 20,
);

I know that I could get the posts in random order like this:

'orderby'                       => 'rand',
'posts_per_page'                => 10,

But how is it possible to combine these two? w Is there a way to store the posts from the first loop and use them in a second loop?