WP_Query: get 3 random posts from 10 latest

There’s one way with:

$args = [
    'post_type'             => 'post',
    'posts_per_page'        => 10,
    'orderby'               => 'date',
    'order'                 => 'DESC',
    'no_found_rows'         => 'true',
    '_shuffle_and_pick'     => 3 // <-- our custom argument
];

$query = new \WP_Query( $args );

where the custom _shuffle_and_pick attribute is supported by this demo plugin:

<?php
/**
 * Plugin Name: Support for the _shuffle_and_pick WP_Query argument.
 */
add_filter( 'the_posts', function( $posts, \WP_Query $query )
{
    if( $pick = $query->get( '_shuffle_and_pick' ) )
    {
        shuffle( $posts );
        $posts = array_slice( $posts, 0, (int) $pick );
    }
    return $posts;
}, 10, 2 );