Query specific number of posts for each post type in specific order

Question

You can use WP_Query() with paged array key to pass the current page number:

<?php
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$args = array(
        'post_type' => 'articles',
        'posts_per_page' => 4,
        'paged' => $paged
    );
$articles = new WP_Query($args);
////////////////////////////////
$args = array(
        'post_type' => 'news',
        'posts_per_page' => 1,
        'meta_query' => array(
            array(
                'key' => 'featured-news',
                'value' => 'Yes',
                'compare' => 'LIKE'
            )
        ),
        'paged' => $paged
    );
$featured = new WP_Query($args);
////////////////////////////////
$args = array(
        'post_type' => 'news',
        'posts_per_page' => 2,
        'meta_query' => array(
            array(
                'key' => 'featured-news',
                'value' => 'No',
                'compare' => 'LIKE'
            )
        ),
        'paged' => $paged
    );
$non_featured = new WP_Query($args);
////////////////////////////////
$articles = objectToArray($articles); // objectToArray() function defines below
$featured = objectToArray($featured);
$non_featured = objectToArray($non_featured);
$all_posts = array_merge($featured, $articles, $non_featured);
?>

And because you are query-ing from 3 post types, pagination will fail, because it doesn’t know from which post type pagination should be based on!

You can use a manual pagination:

<?php
// $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
if($paged > 1)
{
    echo "<a href=\"".home_url("https://wordpress.stackexchange.com/")."/page/".($paged-1)."\">Previous page</a>";
}
echo "<a href=\"".home_url("https://wordpress.stackexchange.com/")."/page/".($paged+1)."\">Next page</a>";
?>

Maybe you want change the HREF attr to something else.

Which I forgot:

<?php
    function objectToArray($d) {
        if (is_object($d)) {
            $d = get_object_vars($d);
        }
        if (is_array($d)) {
            return array_map(__FUNCTION__, $d);
        }
        else {
            return $d;
        }
    }
?>

WP_Query returns a stdClass Object, first you should convert it to an array like below:

<?php
    $articles = objectToArray($articles);
    $featured = objectToArray($featured);
    $non_featured = objectToArray($non_featured);
?>

Then merging them. (updated code above)

Updated

Another handy way is merging stdClass Objects: https://stackoverflow.com/a/1953077/1906508

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