Gumnaam (1965)

After dancing together in a night club, seven young people (five men and two women) are told they have won the night's dance contest and are instructed to board a small plane that will take them to their prize holiday. Instead, they end up stranded on a small island with one of the plane's co-pilots. In search of shelter, the eight go to a mansion where they meet a sinister-looking butler who announces that he knows all them and has been expecting their arrival. After a few musical numbers, castaways begin dropping dead one by one. Who could the killer be, and will any of them escape his grasp?