Isn't this simpler: If we finish 7th, and both the League Cup and FA Cup are won by teams in the top 6 (doesn't matter who), we qualify for Europa.
And if Liverpool win this year's Europa League and finish 5-7, along with the FA Cup and league Cup being won by teams in the top 7, wouldn't 8th qualify for Europa? The PL would get 5 CL spots and 3 Europa spots I think (unless the 3 Europa spots get reduced to 2).