Final answer:
Igor Stravinsky and George Balanchine collaborated on numerous ballets that combined Stravinsky's avant-garde music with Balanchine's neoclassical choreography. The Rite of Spring is one of Stravinsky's most famous works. The exact number of their collaborations is not specified in the materials provided.
Step-by-step explanation:
Igor Stravinsky, a prominent Russian composer, and George Balanchine, a renowned choreographer, collaborated on numerous ballets over the years. Their partnership was notable for its innovative and modernist approach to ballet, combining Stravinsky's avant-garde compositions with Balanchine's neoclassical choreography. One of Stravinsky's most famous and scandalous works for ballet is The Rite of Spring, which shocked audiences with its unconventional rhythms and primitive themes. Stravinsky's collaborations with Balanchine, such as Agon and Apollon Musagète, mark some of the most significant works in 20th-century ballet.
The exact number of ballets Stravinsky and Balanchine worked on together is not provided in the reference materials given, but their partnership is widely documented in the history of dance. Their collaborative works are studied by both ballet enthusiasts and students around the world.