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en.m.wikipedia.org/wiki/Bollywood

The name "Bollywood" is a portmanteau derived from Bombay (the former name for Mumbai) and Hollywood (in California), the center of the American film industry.[14]

https://www.merriam-webster.com/dictionary/Bollywood

Origin and Etymology of bollywood

Bombay (Mumbai), traditional center of the Indian film industry + Hollywood

First Known Use: 1969