Write SQL query to solve given problem: How many female crews are in the movie "Mr. Smith Goes to Washington"?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT COUNT(T3.gender) FROM movie AS T1 INNER JOIN movie_cast AS T2 ON T1.movie_id = T2.movie_id INNER JOIN gender AS T3 ON T2.gender_id = T3.gender_id WHERE T1.title = 'Mr. Smith Goes to Washington' AND T3.gender = 'Female'