Final answer:
Benny Goodman's band had a sudden success with young audiences in California in 1935 primarily due to radio broadcasts and live performances.
Step-by-step explanation:
In 1935, Benny Goodman's band had a sudden success with young audiences in California primarily due to d) Radio broadcasts and live performances. Radio broadcasts allowed the band's music to reach a wide audience and gain popularity, while live performances provided an immersive and exciting experience for the young audience. Through radio and live performances, Goodman's band was able to capture the attention and enthusiasm of young listeners and establish a strong presence within the California music scene.