Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE furniture ( furniture_id number, name text, num_of_component number, market_rate number )
TABLE: CREATE TABLE manufacturer ( manufacturer_id number, open_year number, name text, num_of_factories number, num_of_shops number )
TABLE: CREATE TABLE furniture_manufacte ( manufacturer_id number, furniture_id number, price_in_dollar number )

### Question ###
Find the number of funiture types produced by each manufacturer as well as the company names.

### Accurate SQL ###

SELECT COUNT(*), t1.name FROM manufacturer AS t1 JOIN furniture_manufacte AS t2 ON t1.manufacturer_id = t2.manufacturer_id GROUP BY t1.manufacturer_id