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Get the total count of rows and rows limited by number with same query

Suppose in table A i have many rows with column values a,b,c,d.

Out of these, I want 10 rows with column value 'c' while also counting the total number of rows with column value 'c'.

i tried:

select count(*),* from A where column like 'c'; (without limit)

select count(*),* from A where column like 'c' limit 10;

Is this even possible? or would i have to fire two queries.

SELECT n.*, AA.cnt 
FROM nei_product_background_category c
    INNER JOIN nei_backgrounds n ON n.background_id = c.background_id
    INNER JOIN ( 
        SELECT cc.product_id, COUNT(*) AS cnt 
        FROM nei_product_background_category cc
                    INNER JOIN nei_backgrounds nn ON nn.background_id = cc.background_id
        GROUP BY cc.product_id
    ) AA ON c.product_id = AA.product_id
WHERE
    c.product_id = 578
LIMIT 10

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