The story
From the advertising posters used to promote the 1929 film The Broadway Melody – Hollywood’s first all-talking musical (as opposed to partially talking, partially silent) – which proclaimed the film to be “All Talking All Singing All Dancing” – see film poster. In full, the poster reads: METRO-GOLDWYN-MAYER’S ALL TALKING ALL SINGING ALL DANCING PICTURE THE BROADWAY MELODY
Etymology from Wiktionary, CC BY-SA 4.0.