Question

An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 827 drank alcohol regularly, 645 smoked cigarettes, 183 used illegal drugs, 398 drank alcohol regularly and smoked cigarettes, 112 drank alcohol regularly and used illegal drugs, 108 smoked cigarettes and used illegal drugs, 88 engaged in all three behaviors, and 175 engaged in none of these behaviors.

How many students engaged in at least one of these behaviors?

Answer 1

I think an easy way to approach this is to use a Venn Diagram:
and letting A = drank alcohol, C = smoked cigarettes, D = used illegal drugs

Answer 2

If you know that \(|A \cap C \cap D|\) represents 88, then put that in the middle, then knowing that \(|A \cap C|=398\), \(|A \cap D|=112\), and \(|C \cap D|=108\), then by subtracting 88 from each of those sets, you can find the numbers: 310, 24 and 20 respectively as shown in the diagram: