This one looks like it belongs to the fun math section.
Anyways if you calculate the people who don't have B, F, P, A, L, you'll get
7
10
19
25
38
They sum up to 99. In other words, assume that people who don't have B are not people who don't have F, etc., we know that these 99 people don't have some cars. If you consider some people may not have two or more of these cars, in other words, if there are overlapping, then the total people who don't have BFPALs will be less than 99. The smallest number would be 38, when all those people who don't have B or F or P or A also don't have L.
But anyways, we know that there is at least 1 person who has to have all of the cars, because the most number of people who do not have some of the cars is only 99, 1 less than 100.