How many people for a Top 40 Chart?

I’m wondering how many people were needed to compile a Top 40 radio chart - without more than the odd single “tie” for a chart position - based on listeners calling in to a radio station, not sales. But I lack the mathematical skills to work this out. Obviously, the minimum would be 820 people (if each position differed by a single vote - 40 votes = #1, with each song lower receiving one less vote), but that’s almost impossible statistically.

Can anyone work the math?